import sys
import logging
import itertools
import numpy as np
np.random.seed(0)
import gym
logging.basicConfig(level=logging.INFO,
format='%(asctime)s [%(levelname)s] %(message)s',
stream=sys.stdout, datefmt='%H:%M:%S')
env = gym.make('FrozenLake-v1')
logging.info('observation space = %s', env.observation_space)
logging.info('action space = %s', env.action_space)
logging.info('number of states = %s', env.observation_space.n)
logging.info('number of actions = %s', env.action_space.n)
logging.info('P[14] = %s', env.P[14])
logging.info('P[14][2] = %s', env.P[14][2])
logging.info('reward threshold = %s', env.spec.reward_threshold)
logging.info('max episode steps = %s', env.spec.max_episode_steps)
00:00:00 [INFO] observation space = Discrete(16)
00:00:00 [INFO] action space = Discrete(4)
00:00:00 [INFO] number of states = 16
00:00:00 [INFO] number of actions = 4
00:00:00 [INFO] P[14] = {0: [(0.3333333333333333, 10, 0.0, False), (0.3333333333333333, 13, 0.0, False), (0.3333333333333333, 14, 0.0, False)], 1: [(0.3333333333333333, 13, 0.0, False), (0.3333333333333333, 14, 0.0, False), (0.3333333333333333, 15, 1.0, True)], 2: [(0.3333333333333333, 14, 0.0, False), (0.3333333333333333, 15, 1.0, True), (0.3333333333333333, 10, 0.0, False)], 3: [(0.3333333333333333, 15, 1.0, True), (0.3333333333333333, 10, 0.0, False), (0.3333333333333333, 13, 0.0, False)]}
00:00:00 [INFO] P[14][2] = [(0.3333333333333333, 14, 0.0, False), (0.3333333333333333, 15, 1.0, True), (0.3333333333333333, 10, 0.0, False)]
00:00:00 [INFO] reward threshold = 0.7
00:00:00 [INFO] max episode steps = 100
Play Using Random Policy
def play_policy(env, policy, render=False):
episode_reward = 0.
observation, _ = env.reset()
while True:
if render:
env.render() # render the environment
action = np.random.choice(env.action_space.n, p=policy[observation])
observation, reward, terminated, truncated, _ = env.step(action)
episode_reward += reward
if terminated or truncated:
break
return episode_reward
logging.info('==== Random policy ====')
random_policy = np.ones((env.observation_space.n, env.action_space.n)) / \
env.action_space.n
episode_rewards = [play_policy(env, random_policy) for _ in range(100)]
logging.info('average episode reward = %.2f ± %.2f',
np.mean(episode_rewards), np.std(episode_rewards))
00:00:00 [INFO] ==== Random policy ==== 00:00:00 [INFO] average episode reward = 0.04 ± 0.20
def v2q(env, v, state=None, gamma=1.): # calculate action value from state value
if state is not None: # solve for single state
q = np.zeros(env.action_space.n)
for action in range(env.action_space.n):
for prob, next_state, reward, terminated in env.P[state][action]:
q[action] += prob * \
(reward + gamma * v[next_state] * (1. - terminated))
else: # solve for all states
q = np.zeros((env.observation_space.n, env.action_space.n))
for state in range(env.observation_space.n):
q[state] = v2q(env, v, state, gamma)
return q
def evaluate_policy(env, policy, gamma=1., tolerant=1e-6):
v = np.zeros(env.observation_space.n) # initialize state values
while True:
delta = 0
for state in range(env.observation_space.n):
vs = sum(policy[state] * v2q(env, v, state, gamma)) # update state value
delta = max(delta, abs(v[state]-vs)) # update max error
v[state] = vs
if delta < tolerant: # check whether iterations can finish
break
return v
Evaluate Random Policy
v_random = evaluate_policy(env, random_policy)
logging.info('state value:\n%s', v_random.reshape(4, 4))
q_random = v2q(env, v_random)
logging.info('action value:\n%s', q_random)
00:00:00 [INFO] state value: [[0.0139372 0.01162942 0.02095187 0.01047569] [0.01624741 0. 0.04075119 0. ] [0.03480561 0.08816967 0.14205297 0. ] [0. 0.17582021 0.43929104 0. ]] 00:00:00 [INFO] action value: [[0.01470727 0.01393801 0.01393801 0.01316794] [0.00852221 0.01162969 0.01086043 0.01550616] [0.02444416 0.0209521 0.02405958 0.01435233] [0.01047585 0.01047585 0.00698379 0.01396775] [0.02166341 0.01701767 0.0162476 0.01006154] [0. 0. 0. 0. ] [0.05433495 0.04735099 0.05433495 0.00698396] [0. 0. 0. 0. ] [0.01701767 0.04099176 0.03480569 0.04640756] [0.0702086 0.11755959 0.10595772 0.05895286] [0.18940397 0.17582024 0.16001408 0.04297362] [0. 0. 0. 0. ] [0. 0. 0. 0. ] [0.08799662 0.20503708 0.23442697 0.17582024] [0.25238807 0.53837042 0.52711467 0.43929106] [0. 0. 0. 0. ]]
def improve_policy(env, v, policy, gamma=1.):
optimal = True
for state in range(env.observation_space.n):
q = v2q(env, v, state, gamma)
action = np.argmax(q)
if policy[state][action] != 1.:
optimal = False
policy[state] = 0.
policy[state][action] = 1.
return optimal
Improve from random policy
policy = random_policy.copy()
optimal = improve_policy(env, v_random, policy)
if optimal:
logging.info('No update. Optimal policy is:\n%s', policy)
else:
logging.info('Updating completes. Updated policy is:\n%s', policy)
00:00:00 [INFO] Updating completes. Updated policy is: [[1. 0. 0. 0.] [0. 0. 0. 1.] [1. 0. 0. 0.] [0. 0. 0. 1.] [1. 0. 0. 0.] [1. 0. 0. 0.] [1. 0. 0. 0.] [1. 0. 0. 0.] [0. 0. 0. 1.] [0. 1. 0. 0.] [1. 0. 0. 0.] [1. 0. 0. 0.] [1. 0. 0. 0.] [0. 0. 1. 0.] [0. 1. 0. 0.] [1. 0. 0. 0.]]
def iterate_policy(env, gamma=1., tolerant=1e-6):
policy = np.ones((env.observation_space.n,
env.action_space.n)) / env.action_space.n # initialize
while True:
v = evaluate_policy(env, policy, gamma, tolerant)
if improve_policy(env, v, policy):
break
return policy, v
policy_pi, v_pi = iterate_policy(env)
logging.info('optimal state value =\n%s', v_pi.reshape(4, 4))
logging.info('optimal policy =\n%s', np.argmax(policy_pi, axis=1).reshape(4, 4))
00:00:00 [INFO] optimal state value = [[0.82351246 0.82350689 0.82350303 0.82350106] [0.82351416 0. 0.5294002 0. ] [0.82351683 0.82352026 0.76469786 0. ] [0. 0.88234658 0.94117323 0. ]] 00:00:00 [INFO] optimal policy = [[0 3 3 3] [0 0 0 0] [3 1 0 0] [0 2 1 0]]
Test Policy
episode_rewards = [play_policy(env, policy_pi) for _ in range(100)]
logging.info('average episode reward = %.2f ± %.2f',
np.mean(episode_rewards), np.std(episode_rewards))
00:00:00 [INFO] average episode reward = 0.77 ± 0.42
def iterate_value(env, gamma=1, tolerant=1e-6):
v = np.zeros(env.observation_space.n) # initialization
while True:
delta = 0
for state in range(env.observation_space.n):
vmax = max(v2q(env, v, state, gamma)) # update state value
delta = max(delta, abs(v[state]-vmax))
v[state] = vmax
if delta < tolerant: # check whether iterations can finish
break
# calculate optimal policy
policy = np.zeros((env.observation_space.n, env.action_space.n))
for state in range(env.observation_space.n):
action = np.argmax(v2q(env, v, state, gamma))
policy[state][action] = 1.
return policy, v
policy_vi, v_vi = iterate_value(env)
logging.info('optimal state value =\n%s', v_vi.reshape(4, 4))
logging.info('optimal policy = \n%s', np.argmax(policy_vi, axis=1).reshape(4, 4))
00:00:00 [INFO] optimal state value = [[0.82351232 0.82350671 0.82350281 0.82350083] [0.82351404 0. 0.52940011 0. ] [0.82351673 0.82352018 0.76469779 0. ] [0. 0.88234653 0.94117321 0. ]] 00:00:00 [INFO] optimal policy = [[0 3 3 3] [0 0 0 0] [3 1 0 0] [0 2 1 0]]
Test Policy
episode_rewards = [play_policy(env, policy_vi) for _ in range(100)]
logging.info('average episode reward = %.2f ± %.2f',
np.mean(episode_rewards), np.std(episode_rewards))
00:00:00 [INFO] average episode reward = 0.70 ± 0.46