Play BernoulliMABEnv-v0¶

In [1]:
import sys
import logging

import numpy as np
np.random.seed(0)
import scipy.stats as stats
import gym
import gym.spaces as spaces
import gym.utils.seeding as seeding

logging.basicConfig(level=logging.INFO,
        format='%(asctime)s [%(levelname)s] %(message)s',
        stream=sys.stdout, datefmt='%H:%M:%S')

Environment¶

In [2]:
class BernoulliMABEnv(gym.Env):
    """ Multi-Armed Bandit (MAB) with Bernoulli rewards """

    def __init__(self, n=10, means=None):
        super(BernoulliMABEnv, self).__init__()
        self.observation_space = spaces.Box(low=0, high=0, shape=(0,), dtype=float)
        self.action_space = spaces.Discrete(n)
        self.means = means or self.np_random.random(n)

    def reset(self, *, seed=None, options=None):
        super().reset(seed=seed)
        return np.empty(0, dtype=float), {}

    def step(self, action):
        mean = self.means[action]
        reward = self.np_random.binomial(1, mean)
        observation = np.empty(0, dtype=float)
        return observation, reward, True, False, {}


from gym.envs.registration import register
register(
        id='BernoulliMABEnv-v0',
        entry_point=BernoulliMABEnv,
        )
In [3]:
env = gym.make('BernoulliMABEnv-v0')
for key in vars(env):
    logging.info('%s: %s', key, vars(env)[key])
for key in vars(env.spec):
    logging.info('%s: %s', key, vars(env.spec)[key])

00:00:04 [INFO] action_space: Discrete(10)
00:00:04 [INFO] np_random: RandomState(MT19937)
00:00:04 [INFO] means: [0.05436006 0.96539094 0.63269095 0.29001734 0.10248426 0.67307635
 0.39257674 0.66984607 0.05983897 0.52698724]
00:00:04 [INFO] spec: EnvSpec(BernoulliMABEnv-v0)
00:00:04 [INFO] id: BernoulliMABEnv-v0
00:00:04 [INFO] entry_point: <class '__main__.BernoulliMABEnv'>
00:00:04 [INFO] reward_threshold: None
00:00:04 [INFO] nondeterministic: False
00:00:04 [INFO] max_episode_steps: None
00:00:04 [INFO] _kwargs: {}
00:00:04 [INFO] _env_name: BernoulliMABEnv

Agent¶

$\epsilon$-greedy Agent

In [4]:
class EpsilonGreedyAgent:
    def __init__(self, env):
        self.epsilon = 0.1
        self.action_n = env.action_space.n
        self.counts = np.zeros(self.action_n, dtype=float)
        self.qs = np.zeros(self.action_n, dtype=float)

    def reset(self, mode=None):
        self.mode = mode

    def step(self, observation, reward, terminated):
        if np.random.rand() < self.epsilon:
            action = np.random.randint(self.action_n)
        else:
            action = self.qs.argmax()
        if self.mode == 'train':
            if terminated:
                self.reward = reward  # save reward
            else:
                self.action = action  # save action
        return action

    def close(self):
        if self.mode == 'train':
            self.counts[self.action] += 1
            self.qs[self.action] += (self.reward - self.qs[self.action]) / \
                    self.counts[self.action]

UCB1 Agent

In [5]:
class UCB1Agent:
    def __init__(self, env):
        self.action_n = env.action_space.n
        self.counts = np.zeros(self.action_n, dtype=float)
        self.qs = np.zeros(self.action_n, dtype=float)

    def reset(self, mode=None):
        self.mode = mode

    def step(self, observation, reward, terminated):
        total_count = max(self.counts.sum(), 1)  # lower bounded by 1
        sqrts = np.sqrt(2 * np.log(total_count) / self.counts.clip(min=0.01))
        ucbs = self.qs + sqrts
        action = ucbs.argmax()
        if self.mode == 'train':
            if terminated:
                self.reward = reward  # save reward
            else:
                self.action = action  # save action
        return action

    def close(self):
        if self.mode == 'train':
            self.counts[self.action] += 1
            self.qs[self.action] += (self.reward - self.qs[self.action]) / \
                    self.counts[self.action]

Bayesian UCB Agent

(Use Beta distribution)

In [6]:
class BayesianUCBAgent:
    def __init__(self, env):
        self.action_n = env.action_space.n
        self.alphas = np.ones(self.action_n, dtype=float)
        self.betas = np.ones(self.action_n, dtype=float)

    def reset(self, mode=None):
        self.mode = mode

    def step(self, observation, reward, terminated):
        means = stats.beta.mean(self.alphas, self.betas)
        stds = stats.beta.std(self.alphas, self.betas)
        ucbs = means + 3 * stds
        action = ucbs.argmax()
        if self.mode == 'train':
            if terminated:
                self.reward = reward  # save reward
            else:
                self.action = action  # save action
        return action

    def close(self):
        if self.mode == 'train':
            self.alphas[self.action] += self.reward
            self.betas[self.action] += (1. - self.reward)

Thompson Sampling Agent

(Use Beta distribution)

In [7]:
class ThompsonSamplingAgent:
    def __init__(self, env):
        self.action_n = env.action_space.n
        self.alphas = np.ones(self.action_n, dtype=float)
        self.betas = np.ones(self.action_n, dtype=float)

    def reset(self, mode=None):
        self.mode = mode

    def step(self, observation, reward, terminated):
        samples = [np.random.beta(max(alpha, 1e-6), max(beta, 1e-6))
                for alpha, beta in zip(self.alphas, self.betas)]
        action = np.argmax(samples)
        if self.mode == 'train':
            if terminated:
                self.reward = reward  # save reward
            else:
                self.action = action  # save action
        return action

    def close(self):
        if self.mode == 'train':
            self.alphas[self.action] += self.reward
            self.betas[self.action] += (1. - self.reward)

Online Interaction¶

In [8]:
def play_episode(env, agent, seed=None, mode=None, render=False):
    observation, _ = env.reset(seed=seed)
    reward, terminated, truncated = 0., False, False
    agent.reset(mode=mode)
    episode_reward, elapsed_steps = 0., 0
    while True:
        action = agent.step(observation, reward, terminated)
        if render:
            env.render()
        if terminated or truncated:
            break
        observation, reward, terminated, truncated, _ = env.step(action)
        episode_reward += reward
        elapsed_steps += 1
    agent.close()
    return episode_reward, elapsed_steps


trial_regrets = []
for trial in range(100):
    # create a new agent for each trial - change agent here
    agent = EpsilonGreedyAgent(env)
    agent = UCB1Agent(env)
    agent = BayesianUCBAgent(env)
    agent = ThompsonSamplingAgent(env)

    # train
    episode_rewards = []
    for episode in range(1000):
        episode_reward, elapsed_steps = play_episode(env, agent, seed=episode,
                mode='train')
        episode_rewards.append(episode_reward)
    regrets = env.means.max() - np.array(episode_rewards)
    trial_regret = regrets.sum()
    trial_regrets.append(trial_regret)

    # test
    episode_rewards = []
    for episode in range(100):
        episode_reward, elapsed_steps = play_episode(env, agent)
        episode_rewards.append(episode_reward)
    logging.info('trial %d: average episode reward = %.2f ± %.2f, regret = %.2f',
            trial, np.mean(episode_rewards), np.std(episode_rewards),
            trial_regret)

logging.info('average regret = %.2f ± %.2f',
        np.mean(trial_regrets), np.std(trial_regrets))

00:00:04 [INFO] trial 0: average episode reward = 0.96 ± 0.20, regret = 27.39
00:00:04 [INFO] trial 1: average episode reward = 0.97 ± 0.17, regret = 12.39
00:00:04 [INFO] trial 2: average episode reward = 0.99 ± 0.10, regret = 17.39
00:00:04 [INFO] trial 3: average episode reward = 0.92 ± 0.27, regret = 1.39
00:00:04 [INFO] trial 4: average episode reward = 0.96 ± 0.20, regret = 33.39
00:00:04 [INFO] trial 5: average episode reward = 0.96 ± 0.20, regret = 9.39
00:00:05 [INFO] trial 6: average episode reward = 0.99 ± 0.10, regret = 21.39
00:00:05 [INFO] trial 7: average episode reward = 0.97 ± 0.17, regret = 16.39
00:00:05 [INFO] trial 8: average episode reward = 0.97 ± 0.17, regret = 24.39
00:00:05 [INFO] trial 9: average episode reward = 0.98 ± 0.14, regret = 19.39
00:00:05 [INFO] trial 10: average episode reward = 0.98 ± 0.14, regret = 9.39
00:00:05 [INFO] trial 11: average episode reward = 0.97 ± 0.17, regret = 18.39
00:00:05 [INFO] trial 12: average episode reward = 0.94 ± 0.24, regret = 23.39
00:00:05 [INFO] trial 13: average episode reward = 0.94 ± 0.24, regret = 22.39
00:00:05 [INFO] trial 14: average episode reward = 0.94 ± 0.24, regret = 16.39
00:00:05 [INFO] trial 15: average episode reward = 0.94 ± 0.24, regret = 14.39
00:00:05 [INFO] trial 16: average episode reward = 0.94 ± 0.24, regret = 20.39
00:00:05 [INFO] trial 17: average episode reward = 0.97 ± 0.17, regret = 16.39
00:00:06 [INFO] trial 18: average episode reward = 0.95 ± 0.22, regret = 5.39
00:00:06 [INFO] trial 19: average episode reward = 0.96 ± 0.20, regret = 16.39
00:00:06 [INFO] trial 20: average episode reward = 0.94 ± 0.24, regret = 22.39
00:00:06 [INFO] trial 21: average episode reward = 0.99 ± 0.10, regret = 28.39
00:00:06 [INFO] trial 22: average episode reward = 0.97 ± 0.17, regret = 20.39
00:00:06 [INFO] trial 23: average episode reward = 0.97 ± 0.17, regret = 27.39
00:00:06 [INFO] trial 24: average episode reward = 0.95 ± 0.22, regret = 31.39
00:00:06 [INFO] trial 25: average episode reward = 0.92 ± 0.27, regret = 19.39
00:00:06 [INFO] trial 26: average episode reward = 0.99 ± 0.10, regret = 17.39
00:00:06 [INFO] trial 27: average episode reward = 0.97 ± 0.17, regret = 27.39
00:00:06 [INFO] trial 28: average episode reward = 0.96 ± 0.20, regret = 21.39
00:00:06 [INFO] trial 29: average episode reward = 0.97 ± 0.17, regret = 29.39
00:00:07 [INFO] trial 30: average episode reward = 0.98 ± 0.14, regret = 11.39
00:00:07 [INFO] trial 31: average episode reward = 0.96 ± 0.20, regret = 12.39
00:00:07 [INFO] trial 32: average episode reward = 0.96 ± 0.20, regret = 11.39
00:00:07 [INFO] trial 33: average episode reward = 0.96 ± 0.20, regret = 13.39
00:00:07 [INFO] trial 34: average episode reward = 0.96 ± 0.20, regret = 23.39
00:00:07 [INFO] trial 35: average episode reward = 0.93 ± 0.26, regret = 20.39
00:00:07 [INFO] trial 36: average episode reward = 0.96 ± 0.20, regret = 16.39
00:00:07 [INFO] trial 37: average episode reward = 0.98 ± 0.14, regret = 17.39
00:00:07 [INFO] trial 38: average episode reward = 0.96 ± 0.20, regret = 20.39
00:00:07 [INFO] trial 39: average episode reward = 0.96 ± 0.20, regret = 21.39
00:00:07 [INFO] trial 40: average episode reward = 0.97 ± 0.17, regret = 22.39
00:00:08 [INFO] trial 41: average episode reward = 0.99 ± 0.10, regret = 9.39
00:00:08 [INFO] trial 42: average episode reward = 0.91 ± 0.29, regret = 7.39
00:00:08 [INFO] trial 43: average episode reward = 0.93 ± 0.26, regret = 3.39
00:00:08 [INFO] trial 44: average episode reward = 0.96 ± 0.20, regret = 35.39
00:00:08 [INFO] trial 45: average episode reward = 0.97 ± 0.17, regret = 23.39
00:00:08 [INFO] trial 46: average episode reward = 0.93 ± 0.26, regret = 24.39
00:00:08 [INFO] trial 47: average episode reward = 0.98 ± 0.14, regret = 29.39
00:00:08 [INFO] trial 48: average episode reward = 0.95 ± 0.22, regret = 14.39
00:00:08 [INFO] trial 49: average episode reward = 0.98 ± 0.14, regret = 21.39
00:00:08 [INFO] trial 50: average episode reward = 0.96 ± 0.20, regret = 13.39
00:00:08 [INFO] trial 51: average episode reward = 0.96 ± 0.20, regret = 20.39
00:00:09 [INFO] trial 52: average episode reward = 0.97 ± 0.17, regret = 1.39
00:00:09 [INFO] trial 53: average episode reward = 0.95 ± 0.22, regret = 13.39
00:00:09 [INFO] trial 54: average episode reward = 0.99 ± 0.10, regret = 12.39
00:00:09 [INFO] trial 55: average episode reward = 0.94 ± 0.24, regret = 9.39
00:00:09 [INFO] trial 56: average episode reward = 0.94 ± 0.24, regret = 19.39
00:00:09 [INFO] trial 57: average episode reward = 0.93 ± 0.26, regret = 18.39
00:00:09 [INFO] trial 58: average episode reward = 0.95 ± 0.22, regret = 15.39
00:00:09 [INFO] trial 59: average episode reward = 0.97 ± 0.17, regret = 21.39
00:00:09 [INFO] trial 60: average episode reward = 0.95 ± 0.22, regret = 7.39
00:00:09 [INFO] trial 61: average episode reward = 0.97 ± 0.17, regret = 21.39
00:00:09 [INFO] trial 62: average episode reward = 0.97 ± 0.17, regret = 21.39
00:00:10 [INFO] trial 63: average episode reward = 0.97 ± 0.17, regret = 11.39
00:00:10 [INFO] trial 64: average episode reward = 0.93 ± 0.26, regret = 19.39
00:00:10 [INFO] trial 65: average episode reward = 0.97 ± 0.17, regret = 32.39
00:00:10 [INFO] trial 66: average episode reward = 0.97 ± 0.17, regret = 29.39
00:00:10 [INFO] trial 67: average episode reward = 0.96 ± 0.20, regret = 15.39
00:00:10 [INFO] trial 68: average episode reward = 0.93 ± 0.26, regret = 15.39
00:00:10 [INFO] trial 69: average episode reward = 0.96 ± 0.20, regret = 12.39
00:00:10 [INFO] trial 70: average episode reward = 0.93 ± 0.26, regret = 12.39
00:00:10 [INFO] trial 71: average episode reward = 0.98 ± 0.14, regret = 2.39
00:00:10 [INFO] trial 72: average episode reward = 0.98 ± 0.14, regret = 20.39
00:00:10 [INFO] trial 73: average episode reward = 0.95 ± 0.22, regret = 15.39
00:00:11 [INFO] trial 74: average episode reward = 0.97 ± 0.17, regret = 17.39
00:00:11 [INFO] trial 75: average episode reward = 0.93 ± 0.26, regret = 16.39
00:00:11 [INFO] trial 76: average episode reward = 0.94 ± 0.24, regret = 25.39
00:00:11 [INFO] trial 77: average episode reward = 0.96 ± 0.20, regret = 4.39
00:00:11 [INFO] trial 78: average episode reward = 0.98 ± 0.14, regret = 9.39
00:00:11 [INFO] trial 79: average episode reward = 0.95 ± 0.22, regret = 28.39
00:00:11 [INFO] trial 80: average episode reward = 0.95 ± 0.22, regret = 26.39
00:00:11 [INFO] trial 81: average episode reward = 0.98 ± 0.14, regret = 22.39
00:00:11 [INFO] trial 82: average episode reward = 0.98 ± 0.14, regret = 9.39
00:00:11 [INFO] trial 83: average episode reward = 0.97 ± 0.17, regret = 20.39
00:00:11 [INFO] trial 84: average episode reward = 0.98 ± 0.14, regret = 12.39
00:00:11 [INFO] trial 85: average episode reward = 0.97 ± 0.17, regret = 21.39
00:00:12 [INFO] trial 86: average episode reward = 0.99 ± 0.10, regret = 23.39
00:00:12 [INFO] trial 87: average episode reward = 0.98 ± 0.14, regret = 26.39
00:00:12 [INFO] trial 88: average episode reward = 0.95 ± 0.22, regret = 17.39
00:00:12 [INFO] trial 89: average episode reward = 0.99 ± 0.10, regret = 8.39
00:00:12 [INFO] trial 90: average episode reward = 0.95 ± 0.22, regret = 21.39
00:00:12 [INFO] trial 91: average episode reward = 0.94 ± 0.24, regret = 14.39
00:00:12 [INFO] trial 92: average episode reward = 1.00 ± 0.00, regret = 8.39
00:00:12 [INFO] trial 93: average episode reward = 0.94 ± 0.24, regret = 15.39
00:00:12 [INFO] trial 94: average episode reward = 0.96 ± 0.20, regret = 16.39
00:00:12 [INFO] trial 95: average episode reward = 0.90 ± 0.30, regret = 17.39
00:00:12 [INFO] trial 96: average episode reward = 0.96 ± 0.20, regret = 11.39
00:00:12 [INFO] trial 97: average episode reward = 0.97 ± 0.17, regret = 32.39
00:00:13 [INFO] trial 98: average episode reward = 0.97 ± 0.17, regret = 24.39
00:00:13 [INFO] trial 99: average episode reward = 0.97 ± 0.17, regret = 17.39
00:00:13 [INFO] average regret = 17.99 ± 7.34
In [9]:
env.close()