그로킹 심층 강화학습 중 6장 내용인 “에이전트의 행동 개선”에 대한 내용입니다.
!pip install tqdm numpy scikit-learn pyglet setuptools && \
!pip install gym asciinema pandas tabulate tornado==5.* PyBullet && \
!pip install git+https://github.com/pybox2d/pybox2d#egg=Box2D && \
!pip install git+https://github.com/mimoralea/gym-bandits#egg=gym-bandits && \
!pip install git+https://github.com/mimoralea/gym-walk#egg=gym-walk && \
!pip install git+https://github.com/mimoralea/gym-aima#egg=gym-aima && \
!pip install gym[atari]import warnings ; warnings.filterwarnings('ignore')
import itertools
import gym, gym_walk, gym_aima
import numpy as np
from tabulate import tabulate
from pprint import pprint
from tqdm import tqdm_notebook as tqdm
from itertools import cycle, count
import random
import matplotlib
import matplotlib.pyplot as plt
import matplotlib.pylab as pylab
SEEDS = (12, 34, 56, 78, 90)
%matplotlib inlineplt.style.use('fivethirtyeight')
params = {
'figure.figsize': (15, 8),
'font.size': 24,
'legend.fontsize': 20,
'axes.titlesize': 28,
'axes.labelsize': 24,
'xtick.labelsize': 20,
'ytick.labelsize': 20
}
pylab.rcParams.update(params)
np.set_printoptions(suppress=True)def value_iteration(P, gamma=1.0, theta=1e-10):
V = np.zeros(len(P), dtype=np.float64)
while True:
Q = np.zeros((len(P), len(P[0])), dtype=np.float64)
for s in range(len(P)):
for a in range(len(P[s])):
for prob, next_state, reward, done in P[s][a]:
Q[s][a] += prob * (reward + gamma * V[next_state] * (not done))
if np.max(np.abs(V - np.max(Q, axis=1))) < theta:
break
V = np.max(Q, axis=1)
pi = lambda s: {s:a for s, a in enumerate(np.argmax(Q, axis=1))}[s]
return Q, V, pidef print_policy(pi, P, action_symbols=('<', 'v', '>', '^'), n_cols=4, title='정책:'):
print(title)
arrs = {k:v for k,v in enumerate(action_symbols)}
for s in range(len(P)):
a = pi(s)
print("| ", end="")
if np.all([done for action in P[s].values() for _, _, _, done in action]):
print("".rjust(9), end=" ")
else:
print(str(s).zfill(2), arrs[a].rjust(6), end=" ")
if (s + 1) % n_cols == 0: print("|")def print_state_value_function(V, P, n_cols=4, prec=3, title='상태-가치 함수:'):
print(title)
for s in range(len(P)):
v = V[s]
print("| ", end="")
if np.all([done for action in P[s].values() for _, _, _, done in action]):
print("".rjust(9), end=" ")
else:
print(str(s).zfill(2), '{}'.format(np.round(v, prec)).rjust(6), end=" ")
if (s + 1) % n_cols == 0: print("|")def print_action_value_function(Q,
optimal_Q=None,
action_symbols=('<', '>'),
prec=3,
title='행동-가치 함수:'):
vf_types=('',) if optimal_Q is None else ('', '*', 'er')
headers = ['s',] + [' '.join(i) for i in list(itertools.product(vf_types, action_symbols))]
print(title)
states = np.arange(len(Q))[..., np.newaxis]
arr = np.hstack((states, np.round(Q, prec)))
if not (optimal_Q is None):
arr = np.hstack((arr, np.round(optimal_Q, prec), np.round(optimal_Q-Q, prec)))
print(tabulate(arr, headers, tablefmt="fancy_grid"))def get_policy_metrics(env, gamma, pi, goal_state, optimal_Q,
n_episodes=100, max_steps=200):
random.seed(123); np.random.seed(123) ; env.seed(123)
reached_goal, episode_reward, episode_regret = [], [], []
for _ in range(n_episodes):
state, done, steps = env.reset(), False, 0
episode_reward.append(0.0)
episode_regret.append(0.0)
while not done and steps < max_steps:
action = pi(state)
regret = np.max(optimal_Q[state]) - optimal_Q[state][action]
episode_regret[-1] += regret
state, reward, done, _ = env.step(action)
episode_reward[-1] += (gamma**steps * reward)
steps += 1
reached_goal.append(state == goal_state)
results = np.array((np.sum(reached_goal)/len(reached_goal)*100,
np.mean(episode_reward),
np.mean(episode_regret)))
return resultsdef get_metrics_from_tracks(env, gamma, goal_state, optimal_Q, pi_track, coverage=0.1):
total_samples = len(pi_track)
n_samples = int(total_samples * coverage)
samples_e = np.linspace(0, total_samples, n_samples, endpoint=True, dtype=np.int)
metrics = []
for e, pi in enumerate(tqdm(pi_track)):
if e in samples_e:
metrics.append(get_policy_metrics(
env,
gamma=gamma,
pi=lambda s: pi[s],
goal_state=goal_state,
optimal_Q=optimal_Q))
else:
metrics.append(metrics[-1])
metrics = np.array(metrics)
success_rate_ma, mean_return_ma, mean_regret_ma = np.apply_along_axis(moving_average, axis=0, arr=metrics).T
return success_rate_ma, mean_return_ma, mean_regret_ma def rmse(x, y, dp=4):
return np.round(np.sqrt(np.mean((x - y)**2)), dp)def moving_average(a, n=100) :
ret = np.cumsum(a, dtype=float)
ret[n:] = ret[n:] - ret[:-n]
return ret[n - 1:] / ndef plot_value_function(title, V_track, V_true=None, log=False, limit_value=0.05, limit_items=5):
np.random.seed(123)
per_col = 25
linecycler = cycle(["-","--",":","-."])
legends = []
valid_values = np.argwhere(V_track[-1] > limit_value).squeeze()
items_idxs = np.random.choice(valid_values,
min(len(valid_values), limit_items),
replace=False)
# 첫번째 참값을 뽑아냅니다.
if V_true is not None:
for i, state in enumerate(V_track.T):
if i not in items_idxs:
continue
if state[-1] < limit_value:
continue
label = 'v*({})'.format(i)
plt.axhline(y=V_true[i], color='k', linestyle='-', linewidth=1)
plt.text(int(len(V_track)*1.02), V_true[i]+.01, label)
# 이에 대한 추정치를 계산합니다.
for i, state in enumerate(V_track.T):
if i not in items_idxs:
continue
if state[-1] < limit_value:
continue
line_type = next(linecycler)
label = 'V({})'.format(i)
p, = plt.plot(state, line_type, label=label, linewidth=3)
legends.append(p)
legends.reverse()
ls = []
for loc, idx in enumerate(range(0, len(legends), per_col)):
subset = legends[idx:idx+per_col]
l = plt.legend(subset, [p.get_label() for p in subset],
loc='center right', bbox_to_anchor=(1.25, 0.5))
ls.append(l)
[plt.gca().add_artist(l) for l in ls[:-1]]
if log: plt.xscale('log')
plt.title(title)
plt.ylabel('State-value function')
plt.xlabel('Episodes (log scale)' if log else 'Episodes')
plt.show()def decay_schedule(init_value, min_value, decay_ratio, max_steps, log_start=-2, log_base=10):
decay_steps = int(max_steps * decay_ratio)
rem_steps = max_steps - decay_steps
values = np.logspace(log_start, 0, decay_steps, base=log_base, endpoint=True)[::-1]
values = (values - values.min()) / (values.max() - values.min())
values = (init_value - min_value) * values + min_value
values = np.pad(values, (0, rem_steps), 'edge')
return valuesenv = gym.make('SlipperyWalkSeven-v0')
init_state = env.reset()
goal_state = 8
gamma = 0.99
n_episodes = 3000
P = env.env.P
n_cols, svf_prec, err_prec, avf_prec=9, 4, 2, 3
action_symbols=('<', '>')
limit_items, limit_value = 5, 0.0
cu_limit_items, cu_limit_value, cu_episodes = 10, 0.0, 100plt.plot(decay_schedule(0.5, 0.01, 0.5, n_episodes),
'-', linewidth=2,
label='Alpha schedule')
plt.plot(decay_schedule(1.0, 0.1, 0.9, n_episodes),
':', linewidth=2,
label='Epsilon schedule')
plt.legend(loc=1, ncol=1)
plt.title('Alpha and epsilon schedules')
plt.xlabel('Episodes')
plt.ylabel('Hyperparameter values')
plt.xticks(rotation=45)
plt.show()
optimal_Q, optimal_V, optimal_pi = value_iteration(P, gamma=gamma)
print_state_value_function(optimal_V, P, n_cols=n_cols, prec=svf_prec, title='Optimal state-value function:')
print()
print_action_value_function(optimal_Q,
None,
action_symbols=action_symbols,
prec=avf_prec,
title='Optimal action-value function:')
print()
print_policy(optimal_pi, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_op, mean_return_op, mean_regret_op = get_policy_metrics(
env, gamma=gamma, pi=optimal_pi, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_op, mean_return_op, mean_regret_op))Optimal state-value function:
| | 01 0.5637 | 02 0.763 | 03 0.8449 | 04 0.8892 | 05 0.922 | 06 0.9515 | 07 0.9806 | |
Optimal action-value function:
╒═════╤═══════╤═══════╕
│ s │ < │ > │
╞═════╪═══════╪═══════╡
│ 0 │ 0 │ 0 │
├─────┼───────┼───────┤
│ 1 │ 0.312 │ 0.564 │
├─────┼───────┼───────┤
│ 2 │ 0.67 │ 0.763 │
├─────┼───────┼───────┤
│ 3 │ 0.803 │ 0.845 │
├─────┼───────┼───────┤
│ 4 │ 0.864 │ 0.889 │
├─────┼───────┼───────┤
│ 5 │ 0.901 │ 0.922 │
├─────┼───────┼───────┤
│ 6 │ 0.932 │ 0.952 │
├─────┼───────┼───────┤
│ 7 │ 0.961 │ 0.981 │
├─────┼───────┼───────┤
│ 8 │ 0 │ 0 │
╘═════╧═══════╧═══════╛
정책:
| | 01 > | 02 > | 03 > | 04 > | 05 > | 06 > | 07 > | |
Reaches goal 96.00%. Obtains an average return of 0.8548. Regret of 0.0000def generate_trajectory(select_action, Q, epsilon, env, max_steps=200):
done, trajectory = False, []
while not done:
state = env.reset()
for t in count():
action = select_action(state, Q, epsilon)
next_state, reward, done, _ = env.step(action)
experience = (state, action, reward, next_state, done)
trajectory.append(experience)
if done:
break
if t >= max_steps - 1:
trajectory = []
break
state = next_state
return np.array(trajectory, np.object)def mc_control(env,
gamma=1.0,
init_alpha=0.5,
min_alpha=0.01,
alpha_decay_ratio=0.5,
init_epsilon=1.0,
min_epsilon=0.1,
epsilon_decay_ratio=0.9,
n_episodes=3000,
max_steps=200,
first_visit=True):
nS, nA = env.observation_space.n, env.action_space.n
discounts = np.logspace(0,
max_steps,
num=max_steps,
base=gamma,
endpoint=False)
alphas = decay_schedule(init_alpha,
min_alpha,
alpha_decay_ratio,
n_episodes)
epsilons = decay_schedule(init_epsilon,
min_epsilon,
epsilon_decay_ratio,
n_episodes)
pi_track = []
Q = np.zeros((nS, nA), dtype=np.float64)
Q_track = np.zeros((n_episodes, nS, nA), dtype=np.float64)
select_action = lambda state, Q, epsilon: np.argmax(Q[state]) \
if np.random.random() > epsilon \
else np.random.randint(len(Q[state]))
for e in tqdm(range(n_episodes), leave=False):
trajectory = generate_trajectory(select_action,
Q,
epsilons[e],
env,
max_steps)
visited = np.zeros((nS, nA), dtype=np.bool)
for t, (state, action, reward, _, _) in enumerate(trajectory):
if visited[state][action] and first_visit:
continue
visited[state][action] = True
n_steps = len(trajectory[t:])
G = np.sum(discounts[:n_steps] * trajectory[t:, 2])
Q[state][action] = Q[state][action] + alphas[e] * (G - Q[state][action])
Q_track[e] = Q
pi_track.append(np.argmax(Q, axis=1))
V = np.max(Q, axis=1)
pi = lambda s: {s:a for s, a in enumerate(np.argmax(Q, axis=1))}[s]
return Q, V, pi, Q_track, pi_trackQ_mcs, V_mcs, Q_track_mcs = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_mc, V_mc, pi_mc, Q_track_mc, pi_track_mc = mc_control(env, gamma=gamma, n_episodes=n_episodes)
Q_mcs.append(Q_mc) ; V_mcs.append(V_mc) ; Q_track_mcs.append(Q_track_mc)
Q_mc, V_mc, Q_track_mc = np.mean(Q_mcs, axis=0), np.mean(V_mcs, axis=0), np.mean(Q_track_mcs, axis=0)
del Q_mcs ; del V_mcs ; del Q_track_mcsprint_state_value_function(V_mc, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by FVMC:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_mc - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_mc, optimal_V)))
print()
print_action_value_function(Q_mc,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='FVMC action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_mc, optimal_Q)))
print()
print_policy(pi_mc, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_mc, mean_return_mc, mean_regret_mc = get_policy_metrics(
env, gamma=gamma, pi=pi_mc, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_mc, mean_return_mc, mean_regret_mc))State-value function found by FVMC:
| | 01 0.4895 | 02 0.7209 | 03 0.8311 | 04 0.8766 | 05 0.9137 | 06 0.9463 | 07 0.9788 | |
Optimal state-value function:
| | 01 0.5637 | 02 0.763 | 03 0.8449 | 04 0.8892 | 05 0.922 | 06 0.9515 | 07 0.9806 | |
State-value function errors:
| | 01 -0.07 | 02 -0.04 | 03 -0.01 | 04 -0.01 | 05 -0.01 | 06 -0.01 | 07 -0.0 | |
State-value function RMSE: 0.0293
FVMC action-value function:
╒═════╤═══════╤═══════╤═══════╤═══════╤════════╤════════╕
│ s │ < │ > │ * < │ * > │ er < │ er > │
╞═════╪═══════╪═══════╪═══════╪═══════╪════════╪════════╡
│ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 1 │ 0.194 │ 0.489 │ 0.312 │ 0.564 │ 0.118 │ 0.074 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 2 │ 0.549 │ 0.721 │ 0.67 │ 0.763 │ 0.121 │ 0.042 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 3 │ 0.73 │ 0.831 │ 0.803 │ 0.845 │ 0.073 │ 0.014 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 4 │ 0.843 │ 0.877 │ 0.864 │ 0.889 │ 0.021 │ 0.013 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 5 │ 0.883 │ 0.914 │ 0.901 │ 0.922 │ 0.019 │ 0.008 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 6 │ 0.925 │ 0.946 │ 0.932 │ 0.952 │ 0.007 │ 0.005 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 7 │ 0.955 │ 0.979 │ 0.961 │ 0.981 │ 0.006 │ 0.002 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 8 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
╘═════╧═══════╧═══════╧═══════╧═══════╧════════╧════════╛
Action-value function RMSE: 0.0486
정책:
| | 01 > | 02 > | 03 > | 04 > | 05 > | 06 > | 07 > | |
Reaches goal 96.00%. Obtains an average return of 0.8548. Regret of 0.0000def sarsa(env,
gamma=1.0,
init_alpha=0.5,
min_alpha=0.01,
alpha_decay_ratio=0.5,
init_epsilon=1.0,
min_epsilon=0.1,
epsilon_decay_ratio=0.9,
n_episodes=3000):
nS, nA = env.observation_space.n, env.action_space.n
pi_track = []
Q = np.zeros((nS, nA), dtype=np.float64)
Q_track = np.zeros((n_episodes, nS, nA), dtype=np.float64)
select_action = lambda state, Q, epsilon: np.argmax(Q[state]) \
if np.random.random() > epsilon \
else np.random.randint(len(Q[state]))
alphas = decay_schedule(init_alpha,
min_alpha,
alpha_decay_ratio,
n_episodes)
epsilons = decay_schedule(init_epsilon,
min_epsilon,
epsilon_decay_ratio,
n_episodes)
for e in tqdm(range(n_episodes), leave=False):
state, done = env.reset(), False
action = select_action(state, Q, epsilons[e])
while not done:
next_state, reward, done, _ = env.step(action)
next_action = select_action(next_state, Q, epsilons[e])
td_target = reward + gamma * Q[next_state][next_action] * (not done)
td_error = td_target - Q[state][action]
Q[state][action] = Q[state][action] + alphas[e] * td_error
state, action = next_state, next_action
Q_track[e] = Q
pi_track.append(np.argmax(Q, axis=1))
V = np.max(Q, axis=1)
pi = lambda s: {s:a for s, a in enumerate(np.argmax(Q, axis=1))}[s]
return Q, V, pi, Q_track, pi_trackQ_sarsas, V_sarsas, Q_track_sarsas = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_sarsa, V_sarsa, pi_sarsa, Q_track_sarsa, pi_track_sarsa = sarsa(env, gamma=gamma, n_episodes=n_episodes)
Q_sarsas.append(Q_sarsa) ; V_sarsas.append(V_sarsa) ; Q_track_sarsas.append(Q_track_sarsa)
Q_sarsa = np.mean(Q_sarsas, axis=0)
V_sarsa = np.mean(V_sarsas, axis=0)
Q_track_sarsa = np.mean(Q_track_sarsas, axis=0)
del Q_sarsas ; del V_sarsas ; del Q_track_sarsasprint_state_value_function(V_sarsa, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Sarsa:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_sarsa - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_sarsa, optimal_V)))
print()
print_action_value_function(Q_sarsa,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Sarsa action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_sarsa, optimal_Q)))
print()
print_policy(pi_sarsa, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_sarsa, mean_return_sarsa, mean_regret_sarsa = get_policy_metrics(
env, gamma=gamma, pi=pi_sarsa, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_sarsa, mean_return_sarsa, mean_regret_sarsa))State-value function found by Sarsa:
| | 01 0.461 | 02 0.6868 | 03 0.797 | 04 0.863 | 05 0.9075 | 06 0.9461 | 07 0.9767 | |
Optimal state-value function:
| | 01 0.5637 | 02 0.763 | 03 0.8449 | 04 0.8892 | 05 0.922 | 06 0.9515 | 07 0.9806 | |
State-value function errors:
| | 01 -0.1 | 02 -0.08 | 03 -0.05 | 04 -0.03 | 05 -0.01 | 06 -0.01 | 07 -0.0 | |
State-value function RMSE: 0.0467
Sarsa action-value function:
╒═════╤═══════╤═══════╤═══════╤═══════╤════════╤════════╕
│ s │ < │ > │ * < │ * > │ er < │ er > │
╞═════╪═══════╪═══════╪═══════╪═══════╪════════╪════════╡
│ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 1 │ 0.163 │ 0.461 │ 0.312 │ 0.564 │ 0.149 │ 0.103 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 2 │ 0.5 │ 0.687 │ 0.67 │ 0.763 │ 0.17 │ 0.076 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 3 │ 0.7 │ 0.797 │ 0.803 │ 0.845 │ 0.103 │ 0.048 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 4 │ 0.817 │ 0.863 │ 0.864 │ 0.889 │ 0.047 │ 0.026 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 5 │ 0.874 │ 0.908 │ 0.901 │ 0.922 │ 0.028 │ 0.014 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 6 │ 0.917 │ 0.946 │ 0.932 │ 0.952 │ 0.016 │ 0.005 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 7 │ 0.951 │ 0.977 │ 0.961 │ 0.981 │ 0.01 │ 0.004 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 8 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
╘═════╧═══════╧═══════╧═══════╧═══════╧════════╧════════╛
Action-value function RMSE: 0.0687
정책:
| | 01 > | 02 > | 03 > | 04 > | 05 > | 06 > | 07 > | |
Reaches goal 96.00%. Obtains an average return of 0.8548. Regret of 0.0000def q_learning(env,
gamma=1.0,
init_alpha=0.5,
min_alpha=0.01,
alpha_decay_ratio=0.5,
init_epsilon=1.0,
min_epsilon=0.1,
epsilon_decay_ratio=0.9,
n_episodes=3000):
nS, nA = env.observation_space.n, env.action_space.n
pi_track = []
Q = np.zeros((nS, nA), dtype=np.float64)
Q_track = np.zeros((n_episodes, nS, nA), dtype=np.float64)
select_action = lambda state, Q, epsilon: np.argmax(Q[state]) \
if np.random.random() > epsilon \
else np.random.randint(len(Q[state]))
alphas = decay_schedule(init_alpha,
min_alpha,
alpha_decay_ratio,
n_episodes)
epsilons = decay_schedule(init_epsilon,
min_epsilon,
epsilon_decay_ratio,
n_episodes)
for e in tqdm(range(n_episodes), leave=False):
state, done = env.reset(), False
while not done:
action = select_action(state, Q, epsilons[e])
next_state, reward, done, _ = env.step(action)
td_target = reward + gamma * Q[next_state].max() * (not done)
td_error = td_target - Q[state][action]
Q[state][action] = Q[state][action] + alphas[e] * td_error
state = next_state
Q_track[e] = Q
pi_track.append(np.argmax(Q, axis=1))
V = np.max(Q, axis=1)
pi = lambda s: {s:a for s, a in enumerate(np.argmax(Q, axis=1))}[s]
return Q, V, pi, Q_track, pi_trackQ_qls, V_qls, Q_track_qls = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_ql, V_ql, pi_ql, Q_track_ql, pi_track_ql = q_learning(env, gamma=gamma, n_episodes=n_episodes)
Q_qls.append(Q_ql) ; V_qls.append(V_ql) ; Q_track_qls.append(Q_track_ql)
Q_ql = np.mean(Q_qls, axis=0)
V_ql = np.mean(V_qls, axis=0)
Q_track_ql = np.mean(Q_track_qls, axis=0)
del Q_qls ; del V_qls ; del Q_track_qlsprint_state_value_function(V_ql, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Q-learning:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_ql - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_ql, optimal_V)))
print()
print_action_value_function(Q_ql,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Q-learning action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_ql, optimal_Q)))
print()
print_policy(pi_ql, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_ql, mean_return_ql, mean_regret_ql = get_policy_metrics(
env, gamma=gamma, pi=pi_ql, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_ql, mean_return_ql, mean_regret_ql))State-value function found by Q-learning:
| | 01 0.5523 | 02 0.754 | 03 0.8432 | 04 0.8893 | 05 0.9215 | 06 0.9509 | 07 0.98 | |
Optimal state-value function:
| | 01 0.5637 | 02 0.763 | 03 0.8449 | 04 0.8892 | 05 0.922 | 06 0.9515 | 07 0.9806 | |
State-value function errors:
| | 01 -0.01 | 02 -0.01 | 03 -0.0 | 04 0.0 | 05 -0.0 | 06 -0.0 | 07 -0.0 | |
State-value function RMSE: 0.0049
Q-learning action-value function:
╒═════╤═══════╤═══════╤═══════╤═══════╤════════╤════════╕
│ s │ < │ > │ * < │ * > │ er < │ er > │
╞═════╪═══════╪═══════╪═══════╪═══════╪════════╪════════╡
│ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 1 │ 0.303 │ 0.552 │ 0.312 │ 0.564 │ 0.009 │ 0.011 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 2 │ 0.659 │ 0.754 │ 0.67 │ 0.763 │ 0.011 │ 0.009 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 3 │ 0.795 │ 0.843 │ 0.803 │ 0.845 │ 0.008 │ 0.002 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 4 │ 0.864 │ 0.889 │ 0.864 │ 0.889 │ -0.001 │ -0 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 5 │ 0.901 │ 0.922 │ 0.901 │ 0.922 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 6 │ 0.932 │ 0.951 │ 0.932 │ 0.952 │ 0 │ 0.001 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 7 │ 0.961 │ 0.98 │ 0.961 │ 0.981 │ -0 │ 0.001 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 8 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
╘═════╧═══════╧═══════╧═══════╧═══════╧════════╧════════╛
Action-value function RMSE: 0.0052
정책:
| | 01 > | 02 > | 03 > | 04 > | 05 > | 06 > | 07 > | |
Reaches goal 96.00%. Obtains an average return of 0.8548. Regret of 0.0000def double_q_learning(env,
gamma=1.0,
init_alpha=0.5,
min_alpha=0.01,
alpha_decay_ratio=0.5,
init_epsilon=1.0,
min_epsilon=0.1,
epsilon_decay_ratio=0.9,
n_episodes=3000):
nS, nA = env.observation_space.n, env.action_space.n
pi_track = []
Q1 = np.zeros((nS, nA), dtype=np.float64)
Q2 = np.zeros((nS, nA), dtype=np.float64)
Q_track1 = np.zeros((n_episodes, nS, nA), dtype=np.float64)
Q_track2 = np.zeros((n_episodes, nS, nA), dtype=np.float64)
select_action = lambda state, Q, epsilon: np.argmax(Q[state]) \
if np.random.random() > epsilon \
else np.random.randint(len(Q[state]))
alphas = decay_schedule(init_alpha,
min_alpha,
alpha_decay_ratio,
n_episodes)
epsilons = decay_schedule(init_epsilon,
min_epsilon,
epsilon_decay_ratio,
n_episodes)
for e in tqdm(range(n_episodes), leave=False):
state, done = env.reset(), False
while not done:
action = select_action(state, (Q1 + Q2)/2, epsilons[e])
next_state, reward, done, _ = env.step(action)
if np.random.randint(2):
argmax_Q1 = np.argmax(Q1[next_state])
td_target = reward + gamma * Q2[next_state][argmax_Q1] * (not done)
td_error = td_target - Q1[state][action]
Q1[state][action] = Q1[state][action] + alphas[e] * td_error
else:
argmax_Q2 = np.argmax(Q2[next_state])
td_target = reward + gamma * Q1[next_state][argmax_Q2] * (not done)
td_error = td_target - Q2[state][action]
Q2[state][action] = Q2[state][action] + alphas[e] * td_error
state = next_state
Q_track1[e] = Q1
Q_track2[e] = Q2
pi_track.append(np.argmax((Q1 + Q2)/2, axis=1))
Q = (Q1 + Q2)/2.
V = np.max(Q, axis=1)
pi = lambda s: {s:a for s, a in enumerate(np.argmax(Q, axis=1))}[s]
return Q, V, pi, (Q_track1 + Q_track2)/2., pi_trackQ_dqls, V_dqls, Q_track_dqls = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_dql, V_dql, pi_dql, Q_track_dql, pi_track_dql = double_q_learning(env, gamma=gamma, n_episodes=n_episodes)
Q_dqls.append(Q_dql) ; V_dqls.append(V_dql) ; Q_track_dqls.append(Q_track_dql)
Q_dql, V_dql, Q_track_dql = np.mean(Q_dqls, axis=0), np.mean(V_dqls, axis=0), np.mean(Q_track_dqls, axis=0)
del Q_dqls ; del V_dqls ; del Q_track_dqlsprint_state_value_function(V_dql, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Double Q-Learning:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_dql - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_dql, optimal_V)))
print()
print_action_value_function(Q_dql,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Double Q-Learning action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_dql, optimal_Q)))
print()
print_policy(pi_dql, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_dql, mean_return_dql, mean_regret_dql = get_policy_metrics(
env, gamma=gamma, pi=pi_dql, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_dql, mean_return_dql, mean_regret_dql))State-value function found by Double Q-Learning:
| | 01 0.576 | 02 0.7688 | 03 0.8467 | 04 0.8896 | 05 0.9221 | 06 0.9515 | 07 0.9804 | |
Optimal state-value function:
| | 01 0.5637 | 02 0.763 | 03 0.8449 | 04 0.8892 | 05 0.922 | 06 0.9515 | 07 0.9806 | |
State-value function errors:
| | 01 0.01 | 02 0.01 | 03 0.0 | 04 0.0 | 05 0.0 | 06 -0.0 | 07 -0.0 | |
State-value function RMSE: 0.0046
Double Q-Learning action-value function:
╒═════╤═══════╤═══════╤═══════╤═══════╤════════╤════════╕
│ s │ < │ > │ * < │ * > │ er < │ er > │
╞═════╪═══════╪═══════╪═══════╪═══════╪════════╪════════╡
│ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 1 │ 0.292 │ 0.576 │ 0.312 │ 0.564 │ 0.02 │ -0.012 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 2 │ 0.692 │ 0.769 │ 0.67 │ 0.763 │ -0.021 │ -0.006 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 3 │ 0.811 │ 0.847 │ 0.803 │ 0.845 │ -0.007 │ -0.002 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 4 │ 0.866 │ 0.89 │ 0.864 │ 0.889 │ -0.002 │ -0 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 5 │ 0.903 │ 0.922 │ 0.901 │ 0.922 │ -0.001 │ -0 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 6 │ 0.933 │ 0.951 │ 0.932 │ 0.952 │ -0.001 │ 0 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 7 │ 0.963 │ 0.98 │ 0.961 │ 0.981 │ -0.001 │ 0 │
├─────┼───────┼───────┼───────┼───────┼────────┼────────┤
│ 8 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
╘═════╧═══════╧═══════╧═══════╧═══════╧════════╧════════╛
Action-value function RMSE: 0.0078
정책:
| | 01 > | 02 > | 03 > | 04 > | 05 > | 06 > | 07 > | |
Reaches goal 96.00%. Obtains an average return of 0.8548. Regret of 0.0000plot_value_function(
'FVMC estimates through time vs. true values',
np.max(Q_track_mc, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'FVMC estimates through time vs. true values (log scale)',
np.max(Q_track_mc, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'FVMC estimates through time (close up)',
np.max(Q_track_mc, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
plot_value_function(
'Sarsa estimates through time vs. true values',
np.max(Q_track_sarsa, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'Sarsa estimates through time vs. true values (log scale)',
np.max(Q_track_sarsa, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'Sarsa estimates through time (close up)',
np.max(Q_track_sarsa, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
plot_value_function(
'Q-Learning estimates through time vs. true values',
np.max(Q_track_ql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'Q-Learning estimates through time vs. true values (log scale)',
np.max(Q_track_ql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'Q-Learning estimates through time (close up)',
np.max(Q_track_ql, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
plot_value_function(
'Double Q-Learning estimates through time vs. true values',
np.max(Q_track_dql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'Double Q-Learning estimates through time vs. true values (log scale)',
np.max(Q_track_dql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'Double Q-Learning estimates through time (close up)',
np.max(Q_track_dql, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
mc_success_rate_ma, mc_mean_return_ma, mc_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_mc)sarsa_success_rate_ma, sarsa_mean_return_ma, sarsa_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_sarsa)ql_success_rate_ma, ql_mean_return_ma, ql_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_ql)dql_success_rate_ma, dql_mean_return_ma, dql_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_dql)plt.axhline(y=success_rate_op, color='k', linestyle='-', linewidth=1)
plt.text(int(len(mc_success_rate_ma)*1.02), success_rate_op*1.01, 'π*')
plt.plot(mc_success_rate_ma, '-', linewidth=2, label='FVMC')
plt.plot(sarsa_success_rate_ma, '--', linewidth=2, label='Sarsa')
plt.plot(ql_success_rate_ma, ':', linewidth=2, label='Q-Learning')
plt.plot(dql_success_rate_ma, '-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=4, ncol=1)
plt.title('Policy success rate (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Success rate %')
plt.ylim(-1, 101)
plt.xticks(rotation=45)
plt.show()
plt.axhline(y=mean_return_op, color='k', linestyle='-', linewidth=1)
plt.text(int(len(mc_mean_return_ma)*1.02), mean_return_op*1.01, 'π*')
plt.plot(mc_mean_return_ma, '-', linewidth=2, label='FVMC')
plt.plot(sarsa_mean_return_ma, '--', linewidth=2, label='Sarsa')
plt.plot(ql_mean_return_ma, ':', linewidth=2, label='Q-Learning')
plt.plot(dql_mean_return_ma, '-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=4, ncol=1)
plt.title('Policy episode return (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Return (Gt:T)')
plt.xticks(rotation=45)
plt.show()
plt.plot(mc_mean_regret_ma, '-', linewidth=2, label='FVMC')
plt.plot(sarsa_mean_regret_ma, '--', linewidth=2, label='Sarsa')
plt.plot(ql_mean_regret_ma, ':', linewidth=2, label='Q-Learning')
plt.plot(dql_mean_regret_ma, '-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=1, ncol=1)
plt.title('Policy episode regret (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Regret (q* - Q)')
plt.xticks(rotation=45)
plt.show()
plt.axhline(y=optimal_V[init_state], color='k', linestyle='-', linewidth=1)
plt.text(int(len(Q_track_mc)*1.05), optimal_V[init_state]+.01, 'v*({})'.format(init_state))
plt.plot(moving_average(np.max(Q_track_mc, axis=2).T[init_state]),
'-', linewidth=2, label='FVMC')
plt.plot(moving_average(np.max(Q_track_sarsa, axis=2).T[init_state]),
'--', linewidth=2, label='Sarsa')
plt.plot(moving_average(np.max(Q_track_ql, axis=2).T[init_state]),
':', linewidth=2, label='Q-Learning')
plt.plot(moving_average(np.max(Q_track_dql, axis=2).T[init_state]),
'-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=4, ncol=1)
plt.title('Estimated expected return (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Estimated value of initial state V({})'.format(init_state))
plt.xticks(rotation=45)
plt.show()
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_mc, axis=2) - optimal_V), axis=1)),
'-', linewidth=2, label='FVMC')
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_sarsa, axis=2) - optimal_V), axis=1)),
'--', linewidth=2, label='Sarsa')
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_ql, axis=2) - optimal_V), axis=1)),
':', linewidth=2, label='Q-Learning')
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_dql, axis=2) - optimal_V), axis=1)),
'-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=1, ncol=1)
plt.title('State-value function estimation error (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Mean Absolute Error MAE(V, v*)')
plt.xticks(rotation=45)
plt.show()
plt.plot(moving_average(np.mean(np.abs(Q_track_mc - optimal_Q), axis=(1,2))),
'-', linewidth=2, label='FVMC')
plt.plot(moving_average(np.mean(np.abs(Q_track_sarsa - optimal_Q), axis=(1,2))),
'--', linewidth=2, label='Sarsa')
plt.plot(moving_average(np.mean(np.abs(Q_track_ql - optimal_Q), axis=(1,2))),
':', linewidth=2, label='Q-Learning')
plt.plot(moving_average(np.mean(np.abs(Q_track_dql - optimal_Q), axis=(1,2))),
'-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=1, ncol=1)
plt.title('Action-value function estimation error (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Mean Absolute Error MAE(Q, q*)')
plt.xticks(rotation=45)
plt.show()
env = gym.make('RussellNorvigGridworld-v0')
init_state = env.reset()
goal_state = 3
gamma = 1.0
n_episodes = 4000
P = env.env.P
n_cols, svf_prec, err_prec, avf_prec=4, 4, 2, 3
action_symbols=('<', 'v', '>', '^')
limit_items, limit_value = 5, 0.01
cu_limit_items, cu_limit_value, cu_episodes = 10, 0.0, 1000plt.plot(decay_schedule(0.5, 0.01, 0.5, n_episodes),
'-', linewidth=2,
label='Alpha schedule')
plt.plot(decay_schedule(1.0, 0.1, 0.9, n_episodes),
':', linewidth=2,
label='Epsilon schedule')
plt.legend(loc=1, ncol=1)
plt.title('Alpha and epsilon schedules')
plt.xlabel('Episodes')
plt.ylabel('Hyperparameter values')
plt.xticks(rotation=45)
plt.show()
optimal_Q, optimal_V, optimal_pi = value_iteration(P, gamma=gamma)
print_state_value_function(optimal_V, P, n_cols=n_cols, prec=svf_prec, title='Optimal state-value function:')
print()
print_action_value_function(optimal_Q,
None,
action_symbols=action_symbols,
prec=avf_prec,
title='Optimal action-value function:')
print()
print_policy(optimal_pi, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_op, mean_return_op, mean_regret_op = get_policy_metrics(
env, gamma=gamma, pi=optimal_pi, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_op, mean_return_op, mean_regret_op))Optimal state-value function:
| 00 0.8116 | 01 0.8678 | 02 0.9178 | |
| 04 0.7616 | | 06 0.6603 | |
| 08 0.7053 | 09 0.6553 | 10 0.6114 | 11 0.3879 |
Optimal action-value function:
╒═════╤═══════╤═══════╤════════╤════════╕
│ s │ < │ v │ > │ ^ │
╞═════╪═══════╪═══════╪════════╪════════╡
│ 0 │ 0.767 │ 0.737 │ 0.812 │ 0.777 │
├─────┼───────┼───────┼────────┼────────┤
│ 1 │ 0.783 │ 0.827 │ 0.868 │ 0.827 │
├─────┼───────┼───────┼────────┼────────┤
│ 2 │ 0.812 │ 0.675 │ 0.918 │ 0.881 │
├─────┼───────┼───────┼────────┼────────┤
│ 3 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼────────┼────────┤
│ 4 │ 0.721 │ 0.677 │ 0.721 │ 0.762 │
├─────┼───────┼───────┼────────┼────────┤
│ 5 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼────────┼────────┤
│ 6 │ 0.641 │ 0.415 │ -0.687 │ 0.66 │
├─────┼───────┼───────┼────────┼────────┤
│ 7 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼────────┼────────┤
│ 8 │ 0.671 │ 0.66 │ 0.631 │ 0.705 │
├─────┼───────┼───────┼────────┼────────┤
│ 9 │ 0.655 │ 0.616 │ 0.58 │ 0.616 │
├─────┼───────┼───────┼────────┼────────┤
│ 10 │ 0.611 │ 0.553 │ 0.398 │ 0.593 │
├─────┼───────┼───────┼────────┼────────┤
│ 11 │ 0.388 │ 0.37 │ 0.209 │ -0.74 │
╘═════╧═══════╧═══════╧════════╧════════╛
정책:
| 00 > | 01 > | 02 > | |
| 04 ^ | | 06 ^ | |
| 08 ^ | 09 < | 10 < | 11 < |
Reaches goal 96.00%. Obtains an average return of 0.6424. Regret of 0.0000Q_mcs, V_mcs, Q_track_mcs = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_mc, V_mc, pi_mc, Q_track_mc, pi_track_mc = mc_control(env, gamma=gamma, n_episodes=n_episodes)
Q_mcs.append(Q_mc) ; V_mcs.append(V_mc) ; Q_track_mcs.append(Q_track_mc)
Q_mc, V_mc, Q_track_mc = np.mean(Q_mcs, axis=0), np.mean(V_mcs, axis=0), np.mean(Q_track_mcs, axis=0)
del Q_mcs ; del V_mcs ; del Q_track_mcsprint_state_value_function(V_mc, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by FVMC:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_mc - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_mc, optimal_V)))
print()
print_action_value_function(Q_mc,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='FVMC action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_mc, optimal_Q)))
print()
print_policy(pi_mc, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_mc, mean_return_mc, mean_regret_mc = get_policy_metrics(
env, gamma=gamma, pi=pi_mc, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_mc, mean_return_mc, mean_regret_mc))State-value function found by FVMC:
| 00 0.7899 | 01 0.8518 | 02 0.9191 | |
| 04 0.7349 | | 06 0.6609 | |
| 08 0.6698 | 09 0.5816 | 10 0.2939 | 11 -0.2194 |
Optimal state-value function:
| 00 0.8116 | 01 0.8678 | 02 0.9178 | |
| 04 0.7616 | | 06 0.6603 | |
| 08 0.7053 | 09 0.6553 | 10 0.6114 | 11 0.3879 |
State-value function errors:
| 00 -0.02 | 01 -0.02 | 02 0.0 | |
| 04 -0.03 | | 06 0.0 | |
| 08 -0.04 | 09 -0.07 | 10 -0.32 | 11 -0.61 |
State-value function RMSE: 0.1995
FVMC action-value function:
╒═════╤════════╤════════╤════════╤════════╤═══════╤═══════╤════════╤════════╤════════╤════════╤════════╤════════╕
│ s │ < │ v │ > │ ^ │ * < │ * v │ * > │ * ^ │ er < │ er v │ er > │ er ^ │
╞═════╪════════╪════════╪════════╪════════╪═══════╪═══════╪════════╪════════╪════════╪════════╪════════╪════════╡
│ 0 │ 0.66 │ 0.618 │ 0.79 │ 0.668 │ 0.767 │ 0.737 │ 0.812 │ 0.777 │ 0.106 │ 0.119 │ 0.022 │ 0.109 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 1 │ 0.661 │ 0.747 │ 0.852 │ 0.76 │ 0.783 │ 0.827 │ 0.868 │ 0.827 │ 0.121 │ 0.08 │ 0.016 │ 0.068 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 2 │ 0.727 │ 0.571 │ 0.919 │ 0.816 │ 0.812 │ 0.675 │ 0.918 │ 0.881 │ 0.085 │ 0.104 │ -0.001 │ 0.065 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 3 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 4 │ 0.587 │ 0.542 │ 0.582 │ 0.735 │ 0.721 │ 0.677 │ 0.721 │ 0.762 │ 0.134 │ 0.134 │ 0.138 │ 0.027 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 5 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 6 │ 0.248 │ 0.052 │ -0.698 │ 0.661 │ 0.641 │ 0.415 │ -0.687 │ 0.66 │ 0.393 │ 0.363 │ 0.011 │ -0.001 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 7 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 8 │ 0.541 │ 0.505 │ 0.441 │ 0.67 │ 0.671 │ 0.66 │ 0.631 │ 0.705 │ 0.13 │ 0.155 │ 0.19 │ 0.036 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 9 │ 0.526 │ 0.097 │ 0.132 │ 0.041 │ 0.655 │ 0.616 │ 0.58 │ 0.616 │ 0.13 │ 0.519 │ 0.448 │ 0.575 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 10 │ -0.074 │ -0.218 │ -0.332 │ 0.185 │ 0.611 │ 0.553 │ 0.398 │ 0.593 │ 0.685 │ 0.771 │ 0.73 │ 0.408 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 11 │ -0.242 │ -0.75 │ -0.829 │ -0.905 │ 0.388 │ 0.37 │ 0.209 │ -0.74 │ 0.63 │ 1.12 │ 1.038 │ 0.165 │
╘═════╧════════╧════════╧════════╧════════╧═══════╧═══════╧════════╧════════╧════════╧════════╧════════╧════════╛
Action-value function RMSE: 0.3489
정책:
| 00 > | 01 > | 02 > | |
| 04 ^ | | 06 ^ | |
| 08 ^ | 09 < | 10 < | 11 < |
Reaches goal 96.00%. Obtains an average return of 0.6424. Regret of 0.0000Q_sarsas, V_sarsas, Q_track_sarsas = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_sarsa, V_sarsa, pi_sarsa, Q_track_sarsa, pi_track_sarsa = sarsa(env, gamma=gamma, n_episodes=n_episodes)
Q_sarsas.append(Q_sarsa) ; V_sarsas.append(V_sarsa) ; Q_track_sarsas.append(Q_track_sarsa)
Q_sarsa = np.mean(Q_sarsas, axis=0)
V_sarsa = np.mean(V_sarsas, axis=0)
Q_track_sarsa = np.mean(Q_track_sarsas, axis=0)
del Q_sarsas ; del V_sarsas ; del Q_track_sarsasprint_state_value_function(V_sarsa, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Sarsa:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_sarsa - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_sarsa, optimal_V)))
print()
print_action_value_function(Q_sarsa,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Sarsa action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_sarsa, optimal_Q)))
print()
print_policy(pi_sarsa, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_sarsa, mean_return_sarsa, mean_regret_sarsa = get_policy_metrics(
env, gamma=gamma, pi=pi_sarsa, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_sarsa, mean_return_sarsa, mean_regret_sarsa))State-value function found by Sarsa:
| 00 0.7646 | 01 0.8317 | 02 0.9003 | |
| 04 0.7009 | | 06 0.6164 | |
| 08 0.6212 | 09 0.5314 | 10 0.1956 | 11 -0.4743 |
Optimal state-value function:
| 00 0.8116 | 01 0.8678 | 02 0.9178 | |
| 04 0.7616 | | 06 0.6603 | |
| 08 0.7053 | 09 0.6553 | 10 0.6114 | 11 0.3879 |
State-value function errors:
| 00 -0.05 | 01 -0.04 | 02 -0.02 | |
| 04 -0.06 | | 06 -0.04 | |
| 08 -0.08 | 09 -0.12 | 10 -0.42 | 11 -0.86 |
State-value function RMSE: 0.2811
Sarsa action-value function:
╒═════╤════════╤════════╤════════╤════════╤═══════╤═══════╤════════╤════════╤════════╤════════╤════════╤════════╕
│ s │ < │ v │ > │ ^ │ * < │ * v │ * > │ * ^ │ er < │ er v │ er > │ er ^ │
╞═════╪════════╪════════╪════════╪════════╪═══════╪═══════╪════════╪════════╪════════╪════════╪════════╪════════╡
│ 0 │ 0.645 │ 0.603 │ 0.765 │ 0.667 │ 0.767 │ 0.737 │ 0.812 │ 0.777 │ 0.121 │ 0.134 │ 0.047 │ 0.11 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 1 │ 0.67 │ 0.739 │ 0.832 │ 0.738 │ 0.783 │ 0.827 │ 0.868 │ 0.827 │ 0.113 │ 0.088 │ 0.036 │ 0.089 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 2 │ 0.713 │ 0.492 │ 0.9 │ 0.82 │ 0.812 │ 0.675 │ 0.918 │ 0.881 │ 0.1 │ 0.183 │ 0.018 │ 0.061 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 3 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 4 │ 0.583 │ 0.511 │ 0.586 │ 0.701 │ 0.721 │ 0.677 │ 0.721 │ 0.762 │ 0.138 │ 0.166 │ 0.135 │ 0.061 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 5 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 6 │ 0.221 │ -0.22 │ -0.768 │ 0.616 │ 0.641 │ 0.415 │ -0.687 │ 0.66 │ 0.42 │ 0.635 │ 0.081 │ 0.044 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 7 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 8 │ 0.485 │ 0.468 │ 0.371 │ 0.621 │ 0.671 │ 0.66 │ 0.631 │ 0.705 │ 0.186 │ 0.192 │ 0.26 │ 0.084 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 9 │ 0.531 │ 0.103 │ -0.047 │ 0.125 │ 0.655 │ 0.616 │ 0.58 │ 0.616 │ 0.124 │ 0.513 │ 0.627 │ 0.491 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 10 │ -0.052 │ -0.341 │ -0.722 │ 0.045 │ 0.611 │ 0.553 │ 0.398 │ 0.593 │ 0.663 │ 0.894 │ 1.12 │ 0.548 │
├─────┼────────┼────────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 11 │ -0.474 │ -0.828 │ -0.9 │ -0.976 │ 0.388 │ 0.37 │ 0.209 │ -0.74 │ 0.862 │ 1.198 │ 1.109 │ 0.236 │
╘═════╧════════╧════════╧════════╧════════╧═══════╧═══════╧════════╧════════╧════════╧════════╧════════╧════════╛
Action-value function RMSE: 0.4107
정책:
| 00 > | 01 > | 02 > | |
| 04 ^ | | 06 ^ | |
| 08 ^ | 09 < | 10 ^ | 11 < |
Reaches goal 96.00%. Obtains an average return of 0.6424. Regret of 0.0000Q_qls, V_qls, Q_track_qls = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_ql, V_ql, pi_ql, Q_track_ql, pi_track_ql = q_learning(env, gamma=gamma, n_episodes=n_episodes)
Q_qls.append(Q_ql) ; V_qls.append(V_ql) ; Q_track_qls.append(Q_track_ql)
Q_ql = np.mean(Q_qls, axis=0)
V_ql = np.mean(V_qls, axis=0)
Q_track_ql = np.mean(Q_track_qls, axis=0)
del Q_qls ; del V_qls ; del Q_track_qlsprint_state_value_function(V_ql, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Q-learning:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_ql - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_ql, optimal_V)))
print()
print_action_value_function(Q_ql,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Q-learning action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_ql, optimal_Q)))
print()
print_policy(pi_ql, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_ql, mean_return_ql, mean_regret_ql = get_policy_metrics(
env, gamma=gamma, pi=pi_ql, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_ql, mean_return_ql, mean_regret_ql))State-value function found by Q-learning:
| 00 0.8146 | 01 0.8688 | 02 0.9164 | |
| 04 0.7645 | | 06 0.6005 | |
| 08 0.7068 | 09 0.6558 | 10 0.6114 | 11 0.438 |
Optimal state-value function:
| 00 0.8116 | 01 0.8678 | 02 0.9178 | |
| 04 0.7616 | | 06 0.6603 | |
| 08 0.7053 | 09 0.6553 | 10 0.6114 | 11 0.3879 |
State-value function errors:
| 00 0.0 | 01 0.0 | 02 -0.0 | |
| 04 0.0 | | 06 -0.06 | |
| 08 0.0 | 09 0.0 | 10 0.0 | 11 0.05 |
State-value function RMSE: 0.0225
Q-learning action-value function:
╒═════╤═══════╤═══════╤════════╤════════╤═══════╤═══════╤════════╤════════╤════════╤════════╤════════╤════════╕
│ s │ < │ v │ > │ ^ │ * < │ * v │ * > │ * ^ │ er < │ er v │ er > │ er ^ │
╞═════╪═══════╪═══════╪════════╪════════╪═══════╪═══════╪════════╪════════╪════════╪════════╪════════╪════════╡
│ 0 │ 0.768 │ 0.741 │ 0.815 │ 0.779 │ 0.767 │ 0.737 │ 0.812 │ 0.777 │ -0.002 │ -0.004 │ -0.003 │ -0.002 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 1 │ 0.785 │ 0.828 │ 0.869 │ 0.829 │ 0.783 │ 0.827 │ 0.868 │ 0.827 │ -0.002 │ -0.001 │ -0.001 │ -0.002 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 2 │ 0.812 │ 0.675 │ 0.916 │ 0.882 │ 0.812 │ 0.675 │ 0.918 │ 0.881 │ -0 │ 0 │ 0.001 │ -0.001 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 3 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 4 │ 0.722 │ 0.679 │ 0.722 │ 0.764 │ 0.721 │ 0.677 │ 0.721 │ 0.762 │ -0.001 │ -0.002 │ -0.001 │ -0.003 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 5 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 6 │ 0.582 │ 0.435 │ -0.716 │ 0.593 │ 0.641 │ 0.415 │ -0.687 │ 0.66 │ 0.059 │ -0.02 │ 0.029 │ 0.068 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 7 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 8 │ 0.674 │ 0.664 │ 0.635 │ 0.707 │ 0.671 │ 0.66 │ 0.631 │ 0.705 │ -0.003 │ -0.004 │ -0.004 │ -0.002 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 9 │ 0.656 │ 0.621 │ 0.586 │ 0.623 │ 0.655 │ 0.616 │ 0.58 │ 0.616 │ -0.001 │ -0.005 │ -0.006 │ -0.007 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 10 │ 0.611 │ 0.579 │ 0.463 │ 0.586 │ 0.611 │ 0.553 │ 0.398 │ 0.593 │ -0 │ -0.026 │ -0.065 │ 0.007 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 11 │ 0.402 │ 0.423 │ 0.298 │ -0.795 │ 0.388 │ 0.37 │ 0.209 │ -0.74 │ -0.015 │ -0.052 │ -0.089 │ 0.055 │
╘═════╧═══════╧═══════╧════════╧════════╧═══════╧═══════╧════════╧════════╧════════╧════════╧════════╧════════╛
Action-value function RMSE: 0.0243
정책:
| 00 > | 01 > | 02 > | |
| 04 ^ | | 06 ^ | |
| 08 ^ | 09 < | 10 < | 11 < |
Reaches goal 96.00%. Obtains an average return of 0.6424. Regret of 0.0000Q_dqls, V_dqls, Q_track_dqls = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_dql, V_dql, pi_dql, Q_track_dql, pi_track_dql = double_q_learning(env, gamma=gamma, n_episodes=n_episodes)
Q_dqls.append(Q_dql) ; V_dqls.append(V_dql) ; Q_track_dqls.append(Q_track_dql)
Q_dql, V_dql, Q_track_dql = np.mean(Q_dqls, axis=0), np.mean(V_dqls, axis=0), np.mean(Q_track_dqls, axis=0)
del Q_dqls ; del V_dqls ; del Q_track_dqlsprint_state_value_function(V_dql, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Double Q-Learning:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_dql - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_dql, optimal_V)))
print()
print_action_value_function(Q_dql,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Double Q-Learning action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_dql, optimal_Q)))
print()
print_policy(pi_dql, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_dql, mean_return_dql, mean_regret_dql = get_policy_metrics(
env, gamma=gamma, pi=pi_dql, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_dql, mean_return_dql, mean_regret_dql))State-value function found by Double Q-Learning:
| 00 0.8098 | 01 0.8667 | 02 0.9186 | |
| 04 0.7589 | | 06 0.6613 | |
| 08 0.7035 | 09 0.6532 | 10 0.5885 | 11 0.3222 |
Optimal state-value function:
| 00 0.8116 | 01 0.8678 | 02 0.9178 | |
| 04 0.7616 | | 06 0.6603 | |
| 08 0.7053 | 09 0.6553 | 10 0.6114 | 11 0.3879 |
State-value function errors:
| 00 -0.0 | 01 -0.0 | 02 0.0 | |
| 04 -0.0 | | 06 0.0 | |
| 08 -0.0 | 09 -0.0 | 10 -0.02 | 11 -0.07 |
State-value function RMSE: 0.0201
Double Q-Learning action-value function:
╒═════╤═══════╤═══════╤════════╤════════╤═══════╤═══════╤════════╤════════╤════════╤════════╤════════╤════════╕
│ s │ < │ v │ > │ ^ │ * < │ * v │ * > │ * ^ │ er < │ er v │ er > │ er ^ │
╞═════╪═══════╪═══════╪════════╪════════╪═══════╪═══════╪════════╪════════╪════════╪════════╪════════╪════════╡
│ 0 │ 0.761 │ 0.734 │ 0.81 │ 0.772 │ 0.767 │ 0.737 │ 0.812 │ 0.777 │ 0.005 │ 0.003 │ 0.002 │ 0.005 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 1 │ 0.778 │ 0.821 │ 0.867 │ 0.822 │ 0.783 │ 0.827 │ 0.868 │ 0.827 │ 0.005 │ 0.006 │ 0.001 │ 0.006 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 2 │ 0.807 │ 0.654 │ 0.919 │ 0.875 │ 0.812 │ 0.675 │ 0.918 │ 0.881 │ 0.005 │ 0.021 │ -0.001 │ 0.006 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 3 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 4 │ 0.716 │ 0.673 │ 0.717 │ 0.759 │ 0.721 │ 0.677 │ 0.721 │ 0.762 │ 0.005 │ 0.004 │ 0.004 │ 0.003 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 5 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 6 │ 0.536 │ 0.367 │ -0.689 │ 0.661 │ 0.641 │ 0.415 │ -0.687 │ 0.66 │ 0.105 │ 0.048 │ 0.002 │ -0.001 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 7 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 8 │ 0.665 │ 0.656 │ 0.622 │ 0.704 │ 0.671 │ 0.66 │ 0.631 │ 0.705 │ 0.006 │ 0.004 │ 0.009 │ 0.002 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 9 │ 0.653 │ 0.601 │ 0.534 │ 0.598 │ 0.655 │ 0.616 │ 0.58 │ 0.616 │ 0.002 │ 0.015 │ 0.047 │ 0.017 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 10 │ 0.588 │ 0.458 │ 0.259 │ 0.494 │ 0.611 │ 0.553 │ 0.398 │ 0.593 │ 0.023 │ 0.096 │ 0.138 │ 0.099 │
├─────┼───────┼───────┼────────┼────────┼───────┼───────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 11 │ 0.314 │ 0.13 │ 0.014 │ -0.741 │ 0.388 │ 0.37 │ 0.209 │ -0.74 │ 0.074 │ 0.241 │ 0.196 │ 0.001 │
╘═════╧═══════╧═══════╧════════╧════════╧═══════╧═══════╧════════╧════════╧════════╧════════╧════════╧════════╛
Action-value function RMSE: 0.0572
정책:
| 00 > | 01 > | 02 > | |
| 04 ^ | | 06 ^ | |
| 08 ^ | 09 < | 10 < | 11 < |
Reaches goal 96.00%. Obtains an average return of 0.6424. Regret of 0.0000plot_value_function(
'FVMC estimates through time vs. true values',
np.max(Q_track_mc, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'FVMC estimates through time vs. true values (log scale)',
np.max(Q_track_mc, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'FVMC estimates through time (close up)',
np.max(Q_track_mc, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
plot_value_function(
'Sarsa estimates through time vs. true values',
np.max(Q_track_sarsa, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'Sarsa estimates through time vs. true values (log scale)',
np.max(Q_track_sarsa, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'Sarsa estimates through time (close up)',
np.max(Q_track_sarsa, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
plot_value_function(
'Q-Learning estimates through time vs. true values',
np.max(Q_track_ql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'Q-Learning estimates through time vs. true values (log scale)',
np.max(Q_track_ql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'Q-Learning estimates through time (close up)',
np.max(Q_track_ql, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
plot_value_function(
'Double Q-Learning estimates through time vs. true values',
np.max(Q_track_dql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'Double Q-Learning estimates through time vs. true values (log scale)',
np.max(Q_track_dql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'Double Q-Learning estimates through time (close up)',
np.max(Q_track_dql, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
mc_success_rate_ma, mc_mean_return_ma, mc_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_mc)sarsa_success_rate_ma, sarsa_mean_return_ma, sarsa_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_sarsa)ql_success_rate_ma, ql_mean_return_ma, ql_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_ql)dql_success_rate_ma, dql_mean_return_ma, dql_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_dql)plt.axhline(y=success_rate_op, color='k', linestyle='-', linewidth=1)
plt.text(int(len(mc_success_rate_ma)*1.02), success_rate_op*1.01, 'π*')
plt.plot(mc_success_rate_ma, '-', linewidth=2, label='FVMC')
plt.plot(sarsa_success_rate_ma, '--', linewidth=2, label='Sarsa')
plt.plot(ql_success_rate_ma, ':', linewidth=2, label='Q-Learning')
plt.plot(dql_success_rate_ma, '-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=4, ncol=1)
plt.title('Policy success rate (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Success rate %')
plt.ylim(-1, 101)
plt.xticks(rotation=45)
plt.show()
plt.axhline(y=mean_return_op, color='k', linestyle='-', linewidth=1)
plt.text(int(len(mc_mean_return_ma)*1.02), mean_return_op*1.01, 'π*')
plt.plot(mc_mean_return_ma, '-', linewidth=2, label='FVMC')
plt.plot(sarsa_mean_return_ma, '--', linewidth=2, label='Sarsa')
plt.plot(ql_mean_return_ma, ':', linewidth=2, label='Q-Learning')
plt.plot(dql_mean_return_ma, '-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=4, ncol=1)
plt.title('Policy episode return (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Return (Gt:T)')
plt.xticks(rotation=45)
plt.show()
plt.plot(mc_mean_regret_ma, '-', linewidth=2, label='FVMC')
plt.plot(sarsa_mean_regret_ma, '--', linewidth=2, label='Sarsa')
plt.plot(ql_mean_regret_ma, ':', linewidth=2, label='Q-Learning')
plt.plot(dql_mean_regret_ma, '-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=1, ncol=1)
plt.title('Policy episode regret (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Regret (q* - Q)')
plt.xticks(rotation=45)
plt.show()
plt.axhline(y=optimal_V[init_state], color='k', linestyle='-', linewidth=1)
plt.text(int(len(Q_track_mc)*1.05), optimal_V[init_state]+.01, 'v*({})'.format(init_state))
plt.plot(moving_average(np.max(Q_track_mc, axis=2).T[init_state]),
'-', linewidth=2, label='FVMC')
plt.plot(moving_average(np.max(Q_track_sarsa, axis=2).T[init_state]),
'--', linewidth=2, label='Sarsa')
plt.plot(moving_average(np.max(Q_track_ql, axis=2).T[init_state]),
':', linewidth=2, label='Q-Learning')
plt.plot(moving_average(np.max(Q_track_dql, axis=2).T[init_state]),
'-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=4, ncol=1)
plt.title('Estimated expected return (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Estimated value of initial state V({})'.format(init_state))
plt.xticks(rotation=45)
plt.show()
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_mc, axis=2) - optimal_V), axis=1)),
'-', linewidth=2, label='FVMC')
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_sarsa, axis=2) - optimal_V), axis=1)),
'--', linewidth=2, label='Sarsa')
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_ql, axis=2) - optimal_V), axis=1)),
':', linewidth=2, label='Q-Learning')
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_dql, axis=2) - optimal_V), axis=1)),
'-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=1, ncol=1)
plt.title('State-value function estimation error (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Mean Absolute Error MAE(V, v*)')
plt.xticks(rotation=45)
plt.show()
plt.plot(moving_average(np.mean(np.abs(Q_track_mc - optimal_Q), axis=(1,2))),
'-', linewidth=2, label='FVMC')
plt.plot(moving_average(np.mean(np.abs(Q_track_sarsa - optimal_Q), axis=(1,2))),
'--', linewidth=2, label='Sarsa')
plt.plot(moving_average(np.mean(np.abs(Q_track_ql - optimal_Q), axis=(1,2))),
':', linewidth=2, label='Q-Learning')
plt.plot(moving_average(np.mean(np.abs(Q_track_dql - optimal_Q), axis=(1,2))),
'-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=1, ncol=1)
plt.title('Action-value function estimation error (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Mean Absolute Error MAE(Q, q*)')
plt.xticks(rotation=45)
plt.show()
env = gym.make('FrozenLake-v0')
init_state = env.reset()
goal_state = 15
gamma = 0.99
n_episodes = 10000
P = env.env.P
n_cols, svf_prec, err_prec, avf_prec=4, 4, 2, 3
action_symbols=('<', 'v', '>', '^')
limit_items, limit_value = 5, 0.0
cu_limit_items, cu_limit_value, cu_episodes = 10, 0.01, 2000plt.plot(decay_schedule(0.5, 0.01, 0.5, n_episodes),
'-', linewidth=2,
label='Alpha schedule')
plt.plot(decay_schedule(1.0, 0.1, 0.9, n_episodes),
':', linewidth=2,
label='Epsilon schedule')
plt.legend(loc=1, ncol=1)
plt.title('Alpha and epsilon schedules')
plt.xlabel('Episodes')
plt.ylabel('Hyperparameter values')
plt.xticks(rotation=45)
plt.show()
optimal_Q, optimal_V, optimal_pi = value_iteration(P, gamma=gamma)
print_state_value_function(optimal_V, P, n_cols=n_cols, prec=svf_prec, title='Optimal state-value function:')
print()
print_action_value_function(optimal_Q,
None,
action_symbols=action_symbols,
prec=avf_prec,
title='Optimal action-value function:')
print()
print_policy(optimal_pi, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_op, mean_return_op, mean_regret_op = get_policy_metrics(
env, gamma=gamma, pi=optimal_pi, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_op, mean_return_op, mean_regret_op))Optimal state-value function:
| 00 0.542 | 01 0.4988 | 02 0.4707 | 03 0.4569 |
| 04 0.5585 | | 06 0.3583 | |
| 08 0.5918 | 09 0.6431 | 10 0.6152 | |
| | 13 0.7417 | 14 0.8628 | |
Optimal action-value function:
╒═════╤═══════╤═══════╤═══════╤═══════╕
│ s │ < │ v │ > │ ^ │
╞═════╪═══════╪═══════╪═══════╪═══════╡
│ 0 │ 0.542 │ 0.528 │ 0.528 │ 0.522 │
├─────┼───────┼───────┼───────┼───────┤
│ 1 │ 0.343 │ 0.334 │ 0.32 │ 0.499 │
├─────┼───────┼───────┼───────┼───────┤
│ 2 │ 0.438 │ 0.434 │ 0.424 │ 0.471 │
├─────┼───────┼───────┼───────┼───────┤
│ 3 │ 0.306 │ 0.306 │ 0.302 │ 0.457 │
├─────┼───────┼───────┼───────┼───────┤
│ 4 │ 0.558 │ 0.38 │ 0.374 │ 0.363 │
├─────┼───────┼───────┼───────┼───────┤
│ 5 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┤
│ 6 │ 0.358 │ 0.203 │ 0.358 │ 0.155 │
├─────┼───────┼───────┼───────┼───────┤
│ 7 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┤
│ 8 │ 0.38 │ 0.408 │ 0.397 │ 0.592 │
├─────┼───────┼───────┼───────┼───────┤
│ 9 │ 0.44 │ 0.643 │ 0.448 │ 0.398 │
├─────┼───────┼───────┼───────┼───────┤
│ 10 │ 0.615 │ 0.497 │ 0.403 │ 0.33 │
├─────┼───────┼───────┼───────┼───────┤
│ 11 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┤
│ 12 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┤
│ 13 │ 0.457 │ 0.53 │ 0.742 │ 0.497 │
├─────┼───────┼───────┼───────┼───────┤
│ 14 │ 0.733 │ 0.863 │ 0.821 │ 0.781 │
├─────┼───────┼───────┼───────┼───────┤
│ 15 │ 0 │ 0 │ 0 │ 0 │
╘═════╧═══════╧═══════╧═══════╧═══════╛
정책:
| 00 < | 01 ^ | 02 ^ | 03 ^ |
| 04 < | | 06 < | |
| 08 ^ | 09 v | 10 < | |
| | 13 > | 14 v | |
Reaches goal 74.00%. Obtains an average return of 0.5116. Regret of 0.0000Q_mcs, V_mcs, Q_track_mcs = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_mc, V_mc, pi_mc, Q_track_mc, pi_track_mc = mc_control(env, gamma=gamma, n_episodes=n_episodes)
Q_mcs.append(Q_mc) ; V_mcs.append(V_mc) ; Q_track_mcs.append(Q_track_mc)
Q_mc, V_mc, Q_track_mc = np.mean(Q_mcs, axis=0), np.mean(V_mcs, axis=0), np.mean(Q_track_mcs, axis=0)
del Q_mcs ; del V_mcs ; del Q_track_mcsprint_state_value_function(V_mc, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by FVMC:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_mc - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_mc, optimal_V)))
print()
print_action_value_function(Q_mc,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='FVMC action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_mc, optimal_Q)))
print()
print_policy(pi_mc, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_mc, mean_return_mc, mean_regret_mc = get_policy_metrics(
env, gamma=gamma, pi=pi_mc, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_mc, mean_return_mc, mean_regret_mc))State-value function found by FVMC:
| 00 0.2924 | 01 0.1962 | 02 0.1745 | 03 0.0798 |
| 04 0.3093 | | 06 0.2139 | |
| 08 0.3592 | 09 0.4479 | 10 0.4471 | |
| | 13 0.5975 | 14 0.7784 | |
Optimal state-value function:
| 00 0.542 | 01 0.4988 | 02 0.4707 | 03 0.4569 |
| 04 0.5585 | | 06 0.3583 | |
| 08 0.5918 | 09 0.6431 | 10 0.6152 | |
| | 13 0.7417 | 14 0.8628 | |
State-value function errors:
| 00 -0.25 | 01 -0.3 | 02 -0.3 | 03 -0.38 |
| 04 -0.25 | | 06 -0.14 | |
| 08 -0.23 | 09 -0.2 | 10 -0.17 | |
| | 13 -0.14 | 14 -0.08 | |
State-value function RMSE: 0.1961
FVMC action-value function:
╒═════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤════════╤════════╤════════╤════════╕
│ s │ < │ v │ > │ ^ │ * < │ * v │ * > │ * ^ │ er < │ er v │ er > │ er ^ │
╞═════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪════════╪════════╪════════╪════════╡
│ 0 │ 0.292 │ 0.232 │ 0.239 │ 0.243 │ 0.542 │ 0.528 │ 0.528 │ 0.522 │ 0.25 │ 0.296 │ 0.289 │ 0.279 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 1 │ 0.09 │ 0.108 │ 0.079 │ 0.196 │ 0.343 │ 0.334 │ 0.32 │ 0.499 │ 0.253 │ 0.226 │ 0.241 │ 0.303 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 2 │ 0.149 │ 0.134 │ 0.114 │ 0.109 │ 0.438 │ 0.434 │ 0.424 │ 0.471 │ 0.289 │ 0.3 │ 0.31 │ 0.362 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 3 │ 0.057 │ 0.049 │ 0.013 │ 0.041 │ 0.306 │ 0.306 │ 0.302 │ 0.457 │ 0.25 │ 0.257 │ 0.289 │ 0.416 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 4 │ 0.309 │ 0.203 │ 0.192 │ 0.171 │ 0.558 │ 0.38 │ 0.374 │ 0.363 │ 0.249 │ 0.177 │ 0.182 │ 0.192 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 5 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 6 │ 0.152 │ 0.094 │ 0.18 │ 0.03 │ 0.358 │ 0.203 │ 0.358 │ 0.155 │ 0.207 │ 0.109 │ 0.178 │ 0.125 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 7 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 8 │ 0.189 │ 0.235 │ 0.232 │ 0.359 │ 0.38 │ 0.408 │ 0.397 │ 0.592 │ 0.191 │ 0.172 │ 0.165 │ 0.233 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 9 │ 0.261 │ 0.448 │ 0.317 │ 0.2 │ 0.44 │ 0.643 │ 0.448 │ 0.398 │ 0.179 │ 0.195 │ 0.131 │ 0.198 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 10 │ 0.405 │ 0.34 │ 0.269 │ 0.162 │ 0.615 │ 0.497 │ 0.403 │ 0.33 │ 0.21 │ 0.157 │ 0.134 │ 0.168 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 11 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 12 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 13 │ 0.27 │ 0.378 │ 0.598 │ 0.356 │ 0.457 │ 0.53 │ 0.742 │ 0.497 │ 0.187 │ 0.151 │ 0.144 │ 0.141 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 14 │ 0.543 │ 0.778 │ 0.667 │ 0.607 │ 0.733 │ 0.863 │ 0.821 │ 0.781 │ 0.19 │ 0.084 │ 0.154 │ 0.174 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 15 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
╘═════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧════════╧════════╧════════╧════════╛
Action-value function RMSE: 0.1859
정책:
| 00 < | 01 ^ | 02 > | 03 < |
| 04 < | | 06 < | |
| 08 ^ | 09 v | 10 v | |
| | 13 > | 14 v | |
Reaches goal 62.00%. Obtains an average return of 0.4355. Regret of 0.1419Q_sarsas, V_sarsas, Q_track_sarsas = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_sarsa, V_sarsa, pi_sarsa, Q_track_sarsa, pi_track_sarsa = sarsa(env, gamma=gamma, n_episodes=n_episodes)
Q_sarsas.append(Q_sarsa) ; V_sarsas.append(V_sarsa) ; Q_track_sarsas.append(Q_track_sarsa)
Q_sarsa = np.mean(Q_sarsas, axis=0)
V_sarsa = np.mean(V_sarsas, axis=0)
Q_track_sarsa = np.mean(Q_track_sarsas, axis=0)
del Q_sarsas ; del V_sarsas ; del Q_track_sarsasprint_state_value_function(V_sarsa, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Sarsa:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_sarsa - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_sarsa, optimal_V)))
print()
print_action_value_function(Q_sarsa,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Sarsa action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_sarsa, optimal_Q)))
print()
print_policy(pi_sarsa, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_sarsa, mean_return_sarsa, mean_regret_sarsa = get_policy_metrics(
env, gamma=gamma, pi=pi_sarsa, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_sarsa, mean_return_sarsa, mean_regret_sarsa))State-value function found by Sarsa:
| 00 0.2822 | 01 0.2237 | 02 0.1984 | 03 0.1127 |
| 04 0.3003 | | 06 0.2074 | |
| 08 0.3473 | 09 0.4417 | 10 0.4533 | |
| | 13 0.5771 | 14 0.7754 | |
Optimal state-value function:
| 00 0.542 | 01 0.4988 | 02 0.4707 | 03 0.4569 |
| 04 0.5585 | | 06 0.3583 | |
| 08 0.5918 | 09 0.6431 | 10 0.6152 | |
| | 13 0.7417 | 14 0.8628 | |
State-value function errors:
| 00 -0.26 | 01 -0.28 | 02 -0.27 | 03 -0.34 |
| 04 -0.26 | | 06 -0.15 | |
| 08 -0.24 | 09 -0.2 | 10 -0.16 | |
| | 13 -0.16 | 14 -0.09 | |
State-value function RMSE: 0.1915
Sarsa action-value function:
╒═════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤════════╤════════╤════════╤════════╕
│ s │ < │ v │ > │ ^ │ * < │ * v │ * > │ * ^ │ er < │ er v │ er > │ er ^ │
╞═════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪════════╪════════╪════════╪════════╡
│ 0 │ 0.282 │ 0.257 │ 0.257 │ 0.253 │ 0.542 │ 0.528 │ 0.528 │ 0.522 │ 0.26 │ 0.271 │ 0.271 │ 0.27 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 1 │ 0.118 │ 0.105 │ 0.092 │ 0.224 │ 0.343 │ 0.334 │ 0.32 │ 0.499 │ 0.225 │ 0.229 │ 0.228 │ 0.275 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 2 │ 0.198 │ 0.117 │ 0.115 │ 0.113 │ 0.438 │ 0.434 │ 0.424 │ 0.471 │ 0.24 │ 0.317 │ 0.309 │ 0.358 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 3 │ 0.035 │ 0.033 │ 0.024 │ 0.113 │ 0.306 │ 0.306 │ 0.302 │ 0.457 │ 0.271 │ 0.273 │ 0.277 │ 0.344 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 4 │ 0.3 │ 0.209 │ 0.209 │ 0.188 │ 0.558 │ 0.38 │ 0.374 │ 0.363 │ 0.258 │ 0.171 │ 0.165 │ 0.176 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 5 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 6 │ 0.171 │ 0.114 │ 0.184 │ 0.038 │ 0.358 │ 0.203 │ 0.358 │ 0.155 │ 0.188 │ 0.089 │ 0.174 │ 0.117 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 7 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 8 │ 0.203 │ 0.254 │ 0.235 │ 0.347 │ 0.38 │ 0.408 │ 0.397 │ 0.592 │ 0.177 │ 0.153 │ 0.162 │ 0.244 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 9 │ 0.281 │ 0.442 │ 0.321 │ 0.246 │ 0.44 │ 0.643 │ 0.448 │ 0.398 │ 0.159 │ 0.201 │ 0.127 │ 0.152 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 10 │ 0.453 │ 0.362 │ 0.29 │ 0.166 │ 0.615 │ 0.497 │ 0.403 │ 0.33 │ 0.162 │ 0.135 │ 0.113 │ 0.165 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 11 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 12 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 13 │ 0.305 │ 0.404 │ 0.577 │ 0.367 │ 0.457 │ 0.53 │ 0.742 │ 0.497 │ 0.152 │ 0.125 │ 0.165 │ 0.13 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 14 │ 0.536 │ 0.775 │ 0.703 │ 0.621 │ 0.733 │ 0.863 │ 0.821 │ 0.781 │ 0.197 │ 0.087 │ 0.118 │ 0.161 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 15 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
╘═════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧════════╧════════╧════════╧════════╛
Action-value function RMSE: 0.176
정책:
| 00 < | 01 ^ | 02 < | 03 ^ |
| 04 < | | 06 > | |
| 08 ^ | 09 v | 10 < | |
| | 13 > | 14 v | |
Reaches goal 70.00%. Obtains an average return of 0.4864. Regret of 0.0156Q_qls, V_qls, Q_track_qls = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_ql, V_ql, pi_ql, Q_track_ql, pi_track_ql = q_learning(env, gamma=gamma, n_episodes=n_episodes)
Q_qls.append(Q_ql) ; V_qls.append(V_ql) ; Q_track_qls.append(Q_track_ql)
Q_ql = np.mean(Q_qls, axis=0)
V_ql = np.mean(V_qls, axis=0)
Q_track_ql = np.mean(Q_track_qls, axis=0)
del Q_qls ; del V_qls ; del Q_track_qlsprint_state_value_function(V_ql, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Q-learning:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_ql - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_ql, optimal_V)))
print()
print_action_value_function(Q_ql,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Q-learning action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_ql, optimal_Q)))
print()
print_policy(pi_ql, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_ql, mean_return_ql, mean_regret_ql = get_policy_metrics(
env, gamma=gamma, pi=pi_ql, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_ql, mean_return_ql, mean_regret_ql))State-value function found by Q-learning:
| 00 0.5219 | 01 0.4762 | 02 0.4434 | 03 0.4284 |
| 04 0.539 | | 06 0.3521 | |
| 08 0.5742 | 09 0.6247 | 10 0.6011 | |
| | 13 0.7321 | 14 0.8545 | |
Optimal state-value function:
| 00 0.542 | 01 0.4988 | 02 0.4707 | 03 0.4569 |
| 04 0.5585 | | 06 0.3583 | |
| 08 0.5918 | 09 0.6431 | 10 0.6152 | |
| | 13 0.7417 | 14 0.8628 | |
State-value function errors:
| 00 -0.02 | 01 -0.02 | 02 -0.03 | 03 -0.03 |
| 04 -0.02 | | 06 -0.01 | |
| 08 -0.02 | 09 -0.02 | 10 -0.01 | |
| | 13 -0.01 | 14 -0.01 | |
State-value function RMSE: 0.0156
Q-learning action-value function:
╒═════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤════════╤════════╤════════╤════════╕
│ s │ < │ v │ > │ ^ │ * < │ * v │ * > │ * ^ │ er < │ er v │ er > │ er ^ │
╞═════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪════════╪════════╪════════╪════════╡
│ 0 │ 0.522 │ 0.506 │ 0.506 │ 0.501 │ 0.542 │ 0.528 │ 0.528 │ 0.522 │ 0.02 │ 0.022 │ 0.022 │ 0.022 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 1 │ 0.338 │ 0.324 │ 0.307 │ 0.476 │ 0.343 │ 0.334 │ 0.32 │ 0.499 │ 0.006 │ 0.01 │ 0.013 │ 0.023 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 2 │ 0.429 │ 0.426 │ 0.414 │ 0.443 │ 0.438 │ 0.434 │ 0.424 │ 0.471 │ 0.01 │ 0.008 │ 0.011 │ 0.027 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 3 │ 0.297 │ 0.311 │ 0.289 │ 0.428 │ 0.306 │ 0.306 │ 0.302 │ 0.457 │ 0.009 │ -0.005 │ 0.012 │ 0.028 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 4 │ 0.539 │ 0.368 │ 0.353 │ 0.354 │ 0.558 │ 0.38 │ 0.374 │ 0.363 │ 0.019 │ 0.011 │ 0.021 │ 0.009 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 5 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 6 │ 0.339 │ 0.222 │ 0.331 │ 0.161 │ 0.358 │ 0.203 │ 0.358 │ 0.155 │ 0.02 │ -0.019 │ 0.028 │ -0.005 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 7 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 8 │ 0.379 │ 0.399 │ 0.375 │ 0.574 │ 0.38 │ 0.408 │ 0.397 │ 0.592 │ 0.001 │ 0.009 │ 0.021 │ 0.018 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 9 │ 0.424 │ 0.625 │ 0.437 │ 0.378 │ 0.44 │ 0.643 │ 0.448 │ 0.398 │ 0.016 │ 0.018 │ 0.01 │ 0.021 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 10 │ 0.601 │ 0.484 │ 0.41 │ 0.322 │ 0.615 │ 0.497 │ 0.403 │ 0.33 │ 0.014 │ 0.013 │ -0.007 │ 0.009 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 11 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 12 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 13 │ 0.451 │ 0.534 │ 0.732 │ 0.47 │ 0.457 │ 0.53 │ 0.742 │ 0.497 │ 0.006 │ -0.005 │ 0.01 │ 0.027 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 14 │ 0.724 │ 0.854 │ 0.814 │ 0.774 │ 0.733 │ 0.863 │ 0.821 │ 0.781 │ 0.009 │ 0.008 │ 0.007 │ 0.007 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 15 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
╘═════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧════════╧════════╧════════╧════════╛
Action-value function RMSE: 0.013
정책:
| 00 < | 01 ^ | 02 ^ | 03 ^ |
| 04 < | | 06 < | |
| 08 ^ | 09 v | 10 < | |
| | 13 > | 14 v | |
Reaches goal 74.00%. Obtains an average return of 0.5116. Regret of 0.0000Q_dqls, V_dqls, Q_track_dqls = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_dql, V_dql, pi_dql, Q_track_dql, pi_track_dql = double_q_learning(env, gamma=gamma, n_episodes=n_episodes)
Q_dqls.append(Q_dql) ; V_dqls.append(V_dql) ; Q_track_dqls.append(Q_track_dql)
Q_dql, V_dql, Q_track_dql = np.mean(Q_dqls, axis=0), np.mean(V_dqls, axis=0), np.mean(Q_track_dqls, axis=0)
del Q_dqls ; del V_dqls ; del Q_track_dqlsprint_state_value_function(V_dql, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Double Q-Learning:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_dql - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_dql, optimal_V)))
print()
print_action_value_function(Q_dql,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Double Q-Learning action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_dql, optimal_Q)))
print()
print_policy(pi_dql, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_dql, mean_return_dql, mean_regret_dql = get_policy_metrics(
env, gamma=gamma, pi=pi_dql, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_dql, mean_return_dql, mean_regret_dql))State-value function found by Double Q-Learning:
| 00 0.5184 | 01 0.4354 | 02 0.3635 | 03 0.1936 |
| 04 0.535 | | 06 0.3091 | |
| 08 0.5681 | 09 0.6211 | 10 0.5848 | |
| | 13 0.7279 | 14 0.8563 | |
Optimal state-value function:
| 00 0.542 | 01 0.4988 | 02 0.4707 | 03 0.4569 |
| 04 0.5585 | | 06 0.3583 | |
| 08 0.5918 | 09 0.6431 | 10 0.6152 | |
| | 13 0.7417 | 14 0.8628 | |
State-value function errors:
| 00 -0.02 | 01 -0.06 | 02 -0.11 | 03 -0.26 |
| 04 -0.02 | | 06 -0.05 | |
| 08 -0.02 | 09 -0.02 | 10 -0.03 | |
| | 13 -0.01 | 14 -0.01 | |
State-value function RMSE: 0.0752
Double Q-Learning action-value function:
╒═════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤═══════╤════════╤════════╤════════╤════════╕
│ s │ < │ v │ > │ ^ │ * < │ * v │ * > │ * ^ │ er < │ er v │ er > │ er ^ │
╞═════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪═══════╪════════╪════════╪════════╪════════╡
│ 0 │ 0.518 │ 0.486 │ 0.485 │ 0.482 │ 0.542 │ 0.528 │ 0.528 │ 0.522 │ 0.024 │ 0.042 │ 0.043 │ 0.04 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 1 │ 0.262 │ 0.245 │ 0.201 │ 0.435 │ 0.343 │ 0.334 │ 0.32 │ 0.499 │ 0.081 │ 0.089 │ 0.119 │ 0.063 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 2 │ 0.364 │ 0.226 │ 0.208 │ 0.237 │ 0.438 │ 0.434 │ 0.424 │ 0.471 │ 0.075 │ 0.208 │ 0.216 │ 0.234 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 3 │ 0.076 │ 0.063 │ 0.04 │ 0.171 │ 0.306 │ 0.306 │ 0.302 │ 0.457 │ 0.231 │ 0.243 │ 0.261 │ 0.286 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 4 │ 0.535 │ 0.371 │ 0.354 │ 0.36 │ 0.558 │ 0.38 │ 0.374 │ 0.363 │ 0.023 │ 0.009 │ 0.02 │ 0.003 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 5 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 6 │ 0.273 │ 0.136 │ 0.246 │ 0.069 │ 0.358 │ 0.203 │ 0.358 │ 0.155 │ 0.086 │ 0.067 │ 0.113 │ 0.086 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 7 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 8 │ 0.357 │ 0.387 │ 0.385 │ 0.568 │ 0.38 │ 0.408 │ 0.397 │ 0.592 │ 0.023 │ 0.02 │ 0.011 │ 0.024 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 9 │ 0.41 │ 0.621 │ 0.406 │ 0.358 │ 0.44 │ 0.643 │ 0.448 │ 0.398 │ 0.03 │ 0.022 │ 0.042 │ 0.04 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 10 │ 0.585 │ 0.45 │ 0.359 │ 0.255 │ 0.615 │ 0.497 │ 0.403 │ 0.33 │ 0.03 │ 0.047 │ 0.044 │ 0.076 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 11 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 12 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 13 │ 0.406 │ 0.493 │ 0.728 │ 0.466 │ 0.457 │ 0.53 │ 0.742 │ 0.497 │ 0.051 │ 0.037 │ 0.014 │ 0.031 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 14 │ 0.659 │ 0.856 │ 0.766 │ 0.722 │ 0.733 │ 0.863 │ 0.821 │ 0.781 │ 0.073 │ 0.007 │ 0.055 │ 0.059 │
├─────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┼────────┼────────┼────────┼────────┤
│ 15 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │ 0 │
╘═════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧═══════╧════════╧════════╧════════╧════════╛
Action-value function RMSE: 0.0899
정책:
| 00 < | 01 ^ | 02 < | 03 v |
| 04 < | | 06 > | |
| 08 ^ | 09 v | 10 < | |
| | 13 > | 14 v | |
Reaches goal 70.00%. Obtains an average return of 0.4864. Regret of 0.0156plot_value_function(
'FVMC estimates through time vs. true values',
np.max(Q_track_mc, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'FVMC estimates through time vs. true values (log scale)',
np.max(Q_track_mc, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'FVMC estimates through time (close up)',
np.max(Q_track_mc, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
plot_value_function(
'Sarsa estimates through time vs. true values',
np.max(Q_track_sarsa, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'Sarsa estimates through time vs. true values (log scale)',
np.max(Q_track_sarsa, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'Sarsa estimates through time (close up)',
np.max(Q_track_sarsa, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
plot_value_function(
'Q-Learning estimates through time vs. true values',
np.max(Q_track_ql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'Q-Learning estimates through time vs. true values (log scale)',
np.max(Q_track_ql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'Q-Learning estimates through time (close up)',
np.max(Q_track_ql, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
plot_value_function(
'Double Q-Learning estimates through time vs. true values',
np.max(Q_track_dql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=False)
plot_value_function(
'Double Q-Learning estimates through time vs. true values (log scale)',
np.max(Q_track_dql, axis=2),
optimal_V,
limit_items=limit_items,
limit_value=limit_value,
log=True)
plot_value_function(
'Double Q-Learning estimates through time (close up)',
np.max(Q_track_dql, axis=2)[:cu_episodes],
None,
limit_items=cu_limit_items,
limit_value=cu_limit_value,
log=False)
mc_success_rate_ma, mc_mean_return_ma, mc_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_mc)sarsa_success_rate_ma, sarsa_mean_return_ma, sarsa_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_sarsa)ql_success_rate_ma, ql_mean_return_ma, ql_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_ql)dql_success_rate_ma, dql_mean_return_ma, dql_mean_regret_ma = get_metrics_from_tracks(
env, gamma, goal_state, optimal_Q, pi_track_dql)plt.axhline(y=success_rate_op, color='k', linestyle='-', linewidth=1)
plt.text(int(len(mc_success_rate_ma)*1.02), success_rate_op*1.01, 'π*')
plt.plot(mc_success_rate_ma, '-', linewidth=2, label='FVMC')
plt.plot(sarsa_success_rate_ma, '--', linewidth=2, label='Sarsa')
plt.plot(ql_success_rate_ma, ':', linewidth=2, label='Q-Learning')
plt.plot(dql_success_rate_ma, '-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=4, ncol=1)
plt.title('Policy success rate (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Success rate %')
plt.ylim(-1, 101)
plt.xticks(rotation=45)
plt.show()
plt.axhline(y=mean_return_op, color='k', linestyle='-', linewidth=1)
plt.text(int(len(mc_mean_return_ma)*1.02), mean_return_op*1.01, 'π*')
plt.plot(mc_mean_return_ma, '-', linewidth=2, label='FVMC')
plt.plot(sarsa_mean_return_ma, '--', linewidth=2, label='Sarsa')
plt.plot(ql_mean_return_ma, ':', linewidth=2, label='Q-Learning')
plt.plot(dql_mean_return_ma, '-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=4, ncol=1)
plt.title('Policy episode return (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Return (Gt:T)')
plt.xticks(rotation=45)
plt.show()
plt.plot(mc_mean_regret_ma, '-', linewidth=2, label='FVMC')
plt.plot(sarsa_mean_regret_ma, '--', linewidth=2, label='Sarsa')
plt.plot(ql_mean_regret_ma, ':', linewidth=2, label='Q-Learning')
plt.plot(dql_mean_regret_ma, '-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=1, ncol=1)
plt.title('Policy episode regret (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Regret (q* - Q)')
plt.xticks(rotation=45)
plt.show()
plt.axhline(y=optimal_V[init_state], color='k', linestyle='-', linewidth=1)
plt.text(int(len(Q_track_mc)*1.05), optimal_V[init_state]+.01, 'v*({})'.format(init_state))
plt.plot(moving_average(np.max(Q_track_mc, axis=2).T[init_state]),
'-', linewidth=2, label='FVMC')
plt.plot(moving_average(np.max(Q_track_sarsa, axis=2).T[init_state]),
'--', linewidth=2, label='Sarsa')
plt.plot(moving_average(np.max(Q_track_ql, axis=2).T[init_state]),
':', linewidth=2, label='Q-Learning')
plt.plot(moving_average(np.max(Q_track_dql, axis=2).T[init_state]),
'-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=4, ncol=1)
plt.title('Estimated expected return (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Estimated value of initial state V({})'.format(init_state))
plt.xticks(rotation=45)
plt.show()
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_mc, axis=2) - optimal_V), axis=1)),
'-', linewidth=2, label='FVMC')
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_sarsa, axis=2) - optimal_V), axis=1)),
'--', linewidth=2, label='Sarsa')
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_ql, axis=2) - optimal_V), axis=1)),
':', linewidth=2, label='Q-Learning')
plt.plot(moving_average(np.mean(np.abs(np.max(Q_track_dql, axis=2) - optimal_V), axis=1)),
'-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=1, ncol=1)
plt.title('State-value function estimation error (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Mean Absolute Error MAE(V, v*)')
plt.xticks(rotation=45)
plt.show()
plt.plot(moving_average(np.mean(np.abs(Q_track_mc - optimal_Q), axis=(1,2))),
'-', linewidth=2, label='FVMC')
plt.plot(moving_average(np.mean(np.abs(Q_track_sarsa - optimal_Q), axis=(1,2))),
'--', linewidth=2, label='Sarsa')
plt.plot(moving_average(np.mean(np.abs(Q_track_ql - optimal_Q), axis=(1,2))),
':', linewidth=2, label='Q-Learning')
plt.plot(moving_average(np.mean(np.abs(Q_track_dql - optimal_Q), axis=(1,2))),
'-.', linewidth=2, label='Double Q-Learning')
plt.legend(loc=1, ncol=1)
plt.title('Action-value function estimation error (ma 100)')
plt.xlabel('Episodes')
plt.ylabel('Mean Absolute Error MAE(Q, q*)')
plt.xticks(rotation=45)
plt.show()