Archieving goals more effectively and efficiently
그로킹 심층 강화학습 중 7장 내용인 "조금 더 효율적인 방법으로 목표에 도달하기"에 대한 내용입니다.
- 대체/누적되는 추적을 가진 SARSA($\lambda$), 대체/누적되는 추적을 가진 Q($\lambda$), Dyna-Q, 경로 샘플링
Note: 실행을 위해 아래의 패키지들을 설치해주기 바랍니다.
!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 mpl_toolkits.mplot3d import Axes3D
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 inline
plt.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, pi
def 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 results
def 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:] / n
def 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 plot_transition_model(T_track, episode = 0):
fig = plt.figure(figsize=(20,10))
ax = fig.add_subplot(111, projection='3d')
ax.view_init(elev=20, azim=50)
color_left = '#008fd5' # ax._get_lines.get_next_color()
color_right = '#fc4f30' #ax._get_lines.get_next_color()
left_prob = np.divide(T_track[episode][:,0].T,
T_track[episode][:,0].sum(axis=1).T).T
left_prob = np.nan_to_num(left_prob, 0)
right_prob = np.divide(T_track[episode][:,1].T,
T_track[episode][:,1].sum(axis=1).T).T
right_prob = np.nan_to_num(right_prob, 0)
for s in np.arange(9):
ax.bar3d(s+0.1, np.arange(9)+0.1, np.zeros(9),
np.zeros(9)+0.3,
np.zeros(9)+0.3,
left_prob[s],
color=color_left,
alpha=0.75,
shade=True)
ax.bar3d(s+0.1, np.arange(9)+0.1, left_prob[s],
np.zeros(9)+0.3,
np.zeros(9)+0.3,
right_prob[s],
color=color_right,
alpha=0.75,
shade=True)
ax.tick_params(axis='x', which='major', pad=10)
ax.tick_params(axis='y', which='major', pad=10)
ax.tick_params(axis='z', which='major', pad=10)
ax.xaxis.set_rotate_label(False)
ax.yaxis.set_rotate_label(False)
ax.zaxis.set_rotate_label(False)
ax.set_xticks(np.arange(9))
ax.set_yticks(np.arange(9))
plt.title('SWS learned MDP after {} episodes'.format(episode+1))
ax.set_xlabel('Initial\nstate', labelpad=75, rotation=0)
ax.set_ylabel('Landing\nstate', labelpad=75, rotation=0)
ax.set_zlabel('Transition\nprobabilities', labelpad=75, rotation=0)
left_proxy = plt.Rectangle((0, 0), 1, 1, fc=color_left)
right_proxy = plt.Rectangle((0, 0), 1, 1, fc=color_right)
plt.legend((left_proxy, right_proxy),
('Left', 'Right'),
bbox_to_anchor=(0.15, 0.9),
borderaxespad=0.)
ax.dist = 12
#plt.gcf().subplots_adjust(left=0.1, right=0.9)
plt.tight_layout()
plt.show()
def plot_model_state_sampling(planning, algo='Dyna-Q'):
fig = plt.figure(figsize=(20,10))
color_left = '#008fd5' # ax._get_lines.get_next_color()
color_right = '#fc4f30' #ax._get_lines.get_next_color()
for s in np.arange(9):
actions = planning[np.where(planning[:,0]==s)[0], 1]
left = len(actions[actions == 0])
right = len(actions[actions == 1])
plt.bar(s, right, 0.2, color=color_right)
plt.bar(s, left, 0.2, color=color_left, bottom=right)
plt.title('States samples from {}\nlearned model of SWS environment'.format(algo))
plt.xticks(range(9))
plt.xlabel('Initial states sampled', labelpad=20)
plt.ylabel('Count', labelpad=50, rotation=0)
left_proxy = plt.Rectangle((0, 0), 1, 1, fc=color_left)
right_proxy = plt.Rectangle((0, 0), 1, 1, fc=color_right)
plt.legend((left_proxy, right_proxy),
('Left', 'Right'),
bbox_to_anchor=(0.99, 1.1),
borderaxespad=0.)
#plt.gcf().subplots_adjust(left=0.1, right=0.9)
plt.tight_layout()
plt.show()
def plot_model_state_7(planning, algo='Dyna-Q'):
fig = plt.figure(figsize=(20,10))
color_left = '#008fd5' # ax._get_lines.get_next_color()
color_right = '#fc4f30' #ax._get_lines.get_next_color()
state_7 = planning[np.where(planning[:,0]==7)]
for sp in [6, 7, 8]:
actions = state_7[np.where(state_7[:,3]==sp)[0], 1]
left = len(actions[actions == 0])
right = len(actions[actions == 1])
plt.bar(sp, right, 0.2, color=color_right)
plt.bar(sp, left, 0.2, color=color_left, bottom=right)
plt.title('Next states samples by {}\nin SWS environment from state 7'.format(algo))
plt.xticks([6,7,8])
plt.xlabel('Landing states', labelpad=20)
plt.ylabel('Count', labelpad=50, rotation=0)
left_proxy = plt.Rectangle((0, 0), 1, 1, fc=color_left)
right_proxy = plt.Rectangle((0, 0), 1, 1, fc=color_right)
plt.legend((left_proxy, right_proxy),
('Left', 'Right'),
bbox_to_anchor=(0.99, 1.1),
borderaxespad=0.)
#plt.gcf().subplots_adjust(left=0.1, right=0.9)
plt.tight_layout()
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 values
env = 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, 100
plt.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))
def sarsa_lambda(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,
lambda_=0.5,
replacing_traces=True,
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)
E = np.zeros((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):
E.fill(0)
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]
if replacing_traces: E[state].fill(0)
E[state][action] = E[state][action] + 1
if replacing_traces: E.clip(0, 1, out=E)
Q = Q + alphas[e] * td_error * E
E = gamma * lambda_ * E
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_track
Q_rsls, V_rsls, Q_track_rsls = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_rsl, V_rsl, pi_rsl, Q_track_rsl, pi_track_rsl = sarsa_lambda(env, gamma=gamma, n_episodes=n_episodes)
Q_rsls.append(Q_rsl) ; V_rsls.append(V_rsl) ; Q_track_rsls.append(Q_track_rsl)
Q_rsl, V_rsl, Q_track_rsl = np.mean(Q_rsls, axis=0), np.mean(V_rsls, axis=0), np.mean(Q_track_rsls, axis=0)
del Q_rsls ; del V_rsls ; del Q_track_rsls
print_state_value_function(V_rsl, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Sarsa(λ) replacing:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_rsl - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_rsl, optimal_V)))
print()
print_action_value_function(Q_rsl,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Sarsa(λ) replacing action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_rsl, optimal_Q)))
print()
print_policy(pi_rsl, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_rsl, mean_return_rsl, mean_regret_rsl = get_policy_metrics(
env, gamma=gamma, pi=pi_rsl, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_rsl, mean_return_rsl, mean_regret_rsl))
Q_asls, V_asls, Q_track_asls = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_asl, V_asl, pi_asl, Q_track_asl, pi_track_asl = sarsa_lambda(env, gamma=gamma,
replacing_traces=False,
n_episodes=n_episodes)
Q_asls.append(Q_asl) ; V_asls.append(V_asl) ; Q_track_asls.append(Q_track_asl)
Q_asl, V_asl, Q_track_asl = np.mean(Q_asls, axis=0), np.mean(V_asls, axis=0), np.mean(Q_track_asls, axis=0)
del Q_asls ; del V_asls ; del Q_track_asls
print_state_value_function(V_asl, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Sarsa(λ) accumulating:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_asl - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_asl, optimal_V)))
print()
print_action_value_function(Q_asl,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Sarsa(λ) accumulating action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_asl, optimal_Q)))
print()
print_policy(pi_asl, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_asl, mean_return_asl, mean_regret_asl = get_policy_metrics(
env, gamma=gamma, pi=pi_asl, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_asl, mean_return_asl, mean_regret_asl))
def q_lambda(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,
lambda_=0.5,
replacing_traces=True,
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)
E = np.zeros((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):
E.fill(0)
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])
next_action_is_greedy = Q[next_state][next_action] == Q[next_state].max()
td_target = reward + gamma * Q[next_state].max() * (not done)
td_error = td_target - Q[state][action]
if replacing_traces: E[state].fill(0)
E[state][action] = E[state][action] + 1
if replacing_traces: E.clip(0, 1, out=E)
Q = Q + alphas[e] * td_error * E
if next_action_is_greedy:
E = gamma * lambda_ * E
else:
E.fill(0)
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_track
Q_rqlls, V_rqlls, Q_track_rqlls = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_rqll, V_rqll, pi_rqll, Q_track_rqll, pi_track_rqll = q_lambda(env, gamma=gamma, n_episodes=n_episodes)
Q_rqlls.append(Q_rqll) ; V_rqlls.append(V_rqll) ; Q_track_rqlls.append(Q_track_rqll)
Q_rqll, V_rqll, Q_track_rqll = np.mean(Q_rqlls, axis=0), np.mean(V_rqlls, axis=0), np.mean(Q_track_rqlls, axis=0)
del Q_rqlls ; del V_rqlls ; del Q_track_rqlls
print_state_value_function(V_rqll, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Q(λ) replacing:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_rqll - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_rqll, optimal_V)))
print()
print_action_value_function(Q_rqll,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Q(λ) replacing action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_rqll, optimal_Q)))
print()
print_policy(pi_rqll, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_rqll, mean_return_rqll, mean_regret_rqll = get_policy_metrics(
env, gamma=gamma, pi=pi_rqll, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_rqll, mean_return_rqll, mean_regret_rqll))
Q_aqlls, V_aqlls, Q_track_aqlls = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_aqll, V_aqll, pi_aqll, Q_track_aqll, pi_track_aqll = q_lambda(env, gamma=gamma,
replacing_traces=False,
n_episodes=n_episodes)
Q_aqlls.append(Q_aqll) ; V_aqlls.append(V_aqll) ; Q_track_aqlls.append(Q_track_aqll)
Q_aqll, V_aqll, Q_track_aqll = np.mean(Q_aqlls, axis=0), np.mean(V_aqlls, axis=0), np.mean(Q_track_aqlls, axis=0)
del Q_aqlls ; del V_aqlls ; del Q_track_aqlls
print_state_value_function(V_aqll, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Q(λ) accumulating:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_aqll - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_aqll, optimal_V)))
print()
print_action_value_function(Q_aqll,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Q(λ) accumulating action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_aqll, optimal_Q)))
print()
print_policy(pi_aqll, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_aqll, mean_return_aqll, mean_regret_aqll = get_policy_metrics(
env, gamma=gamma, pi=pi_aqll, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_aqll, mean_return_aqll, mean_regret_aqll))
def dyna_q(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_planning=3,
n_episodes=3000):
nS, nA = env.observation_space.n, env.action_space.n
pi_track, T_track, R_track, planning_track = [], [], [], []
Q = np.zeros((nS, nA), dtype=np.float64)
T_count = np.zeros((nS, nA, nS), dtype=np.int)
R_model = np.zeros((nS, nA, nS), 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)
T_count[state][action][next_state] += 1
r_diff = reward - R_model[state][action][next_state]
R_model[state][action][next_state] += (r_diff / T_count[state][action][next_state])
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
backup_next_state = next_state
for _ in range(n_planning):
if Q.sum() == 0: break
visited_states = np.where(np.sum(T_count, axis=(1, 2)) > 0)[0]
state = np.random.choice(visited_states)
actions_taken = np.where(np.sum(T_count[state], axis=1) > 0)[0]
action = np.random.choice(actions_taken)
probs = T_count[state][action]/T_count[state][action].sum()
next_state = np.random.choice(np.arange(nS), size=1, p=probs)[0]
reward = R_model[state][action][next_state]
planning_track.append((state, action, reward, next_state))
td_target = reward + gamma * Q[next_state].max()
td_error = td_target - Q[state][action]
Q[state][action] = Q[state][action] + alphas[e] * td_error
state = backup_next_state
T_track.append(T_count.copy())
R_track.append(R_model.copy())
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_track, T_track, R_track, np.array(planning_track)
Q_dqs, V_dqs, Q_track_dqs = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_dq, V_dq, pi_dq, Q_track_dq, pi_track_dq, T_track_dq, R_track_dq, planning_dq = dyna_q(
env, gamma=gamma, n_episodes=n_episodes)
Q_dqs.append(Q_dq) ; V_dqs.append(V_dq) ; Q_track_dqs.append(Q_track_dq)
Q_dq, V_dq, Q_track_dq = np.mean(Q_dqs, axis=0), np.mean(V_dqs, axis=0), np.mean(Q_track_dqs, axis=0)
del Q_dqs ; del V_dqs ; del Q_track_dqs
print_state_value_function(V_dq, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Dyna-Q:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_dq - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_dq, optimal_V)))
print()
print_action_value_function(Q_dq,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Dyna-Q action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_dq, optimal_Q)))
print()
print_policy(pi_dq, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_dq, mean_return_dq, mean_regret_dq = get_policy_metrics(
env, gamma=gamma, pi=pi_dq, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_dq, mean_return_dq, mean_regret_dq))
plot_transition_model(T_track_dq, episode=0)
plot_transition_model(T_track_dq, episode=9)
plot_transition_model(T_track_dq, episode=99)
plot_transition_model(T_track_dq, episode=len(T_track_dq)-1)
plot_model_state_sampling(planning_dq, algo='Dyna-Q')
plot_model_state_7(planning_dq, algo='Dyna-Q')
def trajectory_sampling(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,
max_trajectory_depth=100,
planning_freq=5,
greedy_planning=True,
n_episodes=3000):
nS, nA = env.observation_space.n, env.action_space.n
pi_track, T_track, R_track, planning_track = [], [], [], []
Q = np.zeros((nS, nA), dtype=np.float64)
T_count = np.zeros((nS, nA, nS), dtype=np.int)
R_model = np.zeros((nS, nA, nS), 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)
T_count[state][action][next_state] += 1
r_diff = reward - R_model[state][action][next_state]
R_model[state][action][next_state] += (r_diff / T_count[state][action][next_state])
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
backup_next_state = next_state
if e % planning_freq == 0:
for _ in range(max_trajectory_depth):
if Q.sum() == 0: break
action = Q[state].argmax() if greedy_planning else \
select_action(state, Q, epsilons[e])
if not T_count[state][action].sum(): break
probs = T_count[state][action]/T_count[state][action].sum()
next_state = np.random.choice(np.arange(nS), size=1, p=probs)[0]
reward = R_model[state][action][next_state]
planning_track.append((state, action, reward, next_state))
td_target = reward + gamma * Q[next_state].max()
td_error = td_target - Q[state][action]
Q[state][action] = Q[state][action] + alphas[e] * td_error
state = next_state
state = backup_next_state
T_track.append(T_count.copy())
R_track.append(R_model.copy())
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_track, T_track, R_track, np.array(planning_track)
Q_tss, V_tss, Q_track_tss = [], [], []
for seed in tqdm(SEEDS, desc='All seeds', leave=True):
random.seed(seed); np.random.seed(seed) ; env.seed(seed)
Q_ts, V_ts, pi_ts, Q_track_ts, pi_track_ts, T_track_ts, R_track_ts, planning_ts = trajectory_sampling(
env, gamma=gamma, n_episodes=n_episodes)
Q_tss.append(Q_ts) ; V_tss.append(V_ts) ; Q_track_tss.append(Q_track_ts)
Q_ts, V_ts, Q_track_ts = np.mean(Q_tss, axis=0), np.mean(V_tss, axis=0), np.mean(Q_track_tss, axis=0)
del Q_tss ; del V_tss ; del Q_track_tss
print_state_value_function(V_ts, P, n_cols=n_cols,
prec=svf_prec, title='State-value function found by Trajectory Sampling:')
print_state_value_function(optimal_V, P, n_cols=n_cols,
prec=svf_prec, title='Optimal state-value function:')
print_state_value_function(V_ts - optimal_V, P, n_cols=n_cols,
prec=err_prec, title='State-value function errors:')
print('State-value function RMSE: {}'.format(rmse(V_ts, optimal_V)))
print()
print_action_value_function(Q_ts,
optimal_Q,
action_symbols=action_symbols,
prec=avf_prec,
title='Trajectory Sampling action-value function:')
print('Action-value function RMSE: {}'.format(rmse(Q_ts, optimal_Q)))
print()
print_policy(pi_ts, P, action_symbols=action_symbols, n_cols=n_cols)
success_rate_ts, mean_return_ts, mean_regret_ts = get_policy_metrics(
env, gamma=gamma, pi=pi_ts, goal_state=goal_state, optimal_Q=optimal_Q)
print('Reaches goal {:.2f}%. Obtains an average return of {:.4f}. Regret of {:.4f}'.format(
success_rate_ts, mean_return_ts, mean_regret_ts))
plot_model_state_sampling(planning_ts, algo='Trajectory Sampling')