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bandit.py
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bandit.py
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# Heavily inspired from Jaromir Janisch (https://github.com/jaromiru)
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import numpy as np
from tqdm import tqdm
class Bandit:
def __init__(self, k_arm=10, strategy ='epsilon-greedy', update_mode = 'average',
epsilon = 0.1, UCB = 0.4, step_size = 0.1, initial = 0):
# k_arm: number of arms
self.k = k_arm
self.time = 0
self.total_reward = 0
# First dimension, what strategy are we using during training: 'epsilon-greedy' or 'UCB'
self.strategy = strategy
# Second dimension, how do we update estimates: 'average' or 'step_size'
self.update_mode = update_mode
# Parameters
self.epsilon = epsilon
self.UCB = UCB
self.step_size = step_size
self.initial = initial
def reset(self):
# reward for each action
self.q_true = np.random.randn(self.k)
self.best_action = np.argmax(self.q_true)
# estimation for each action
self.q_estimation = np.zeros(self.k) + self.initial
# number of times each action was chosen
self.action_count = np.zeros(self.k)
def choose_action(self):
if self.strategy == 'epsilon-greedy':
# using the epsilon-greedy strategy
if np.random.rand() < self.epsilon:
return np.random.randint(self.k)
q_best = np.max(self.q_estimation)
return np.random.choice([action for action, q in enumerate(self.q_estimation) if q == q_best])
if self.strategy == 'UCB':
# using the UCB algorithm
if np.all(self.action_count != 0):
UCB_estimation = self.q_estimation + self.UCB * np.sqrt(np.log(self.time + 1) / self.action_count)
q_best = np.max(UCB_estimation)
return np.random.choice([action for action, q in enumerate(UCB_estimation) if q == q_best])
else:
return np.random.choice([action for action in np.arange(self.k) if self.action_count[action] == 0])
def update(self, action):
# play an action and update the estimation for this action
# generate the reward under using a Gaussian distribution centered around the reward with standard deviation 1
reward = self.q_true[action] + np.random.randn()
self.time += 1
self.total_reward += reward
self.action_count[action] += 1
if self.update_mode == 'average':
# update using sample averages
self.q_estimation[action] += 1.0 / self.action_count[action] * (reward - self.q_estimation[action])
if self.update_mode == 'step_size':
# update with constant step size
self.q_estimation[action] += self.step_size * (reward - self.q_estimation[action])
return reward
def simulate(runs, time, bandits):
best_action_counts = np.zeros((len(bandits), runs, time))
rewards = np.zeros(best_action_counts.shape)
for i, bandit in enumerate(bandits):
for r in tqdm(range(runs)):
bandit.reset()
for t in range(time):
action = bandit.choose_action()
reward = bandit.update(action)
rewards[i, r, t] = reward
if action == bandit.best_action:
best_action_counts[i, r, t] = 1
best_action_counts = best_action_counts.mean(axis=1)
rewards = rewards.mean(axis=1)
return best_action_counts, rewards
def illustration_rewards():
plt.violinplot(dataset=np.random.randn(200,10) + np.random.randn(10))
plt.xlabel("Action")
plt.ylabel("Reward distribution")
plt.savefig('1_illustration_rewards.png')
plt.close()
def parameter_epsilon(runs=2000, time=1000):
epsilons = [0, 0.01, 0.1, 0.2]
bandits = [Bandit(epsilon = eps) for eps in epsilons]
best_action_counts,rewards = simulate(runs, time, bandits)
for eps, rewards in zip(epsilons, rewards):
plt.plot(rewards / time, label='epsilon = %.02f' % (eps))
plt.xlabel('Steps')
plt.ylabel('Average reward')
plt.legend()
plt.savefig('2_epsilon-greedy_average_reward.png')
plt.close()
for eps, counts in zip(epsilons, best_action_counts):
plt.plot(counts, label='epsilon = %.02f' % (eps))
plt.xlabel('Steps')
plt.ylabel('% optimal action')
plt.legend()
plt.savefig('3_epsilon-greedy_best_actions_count.png')
plt.close()
def parameter_UCB(runs=2000, time=1000):
UCBs = np.arange(0, 1, step = 0.4, dtype=np.float)
bandits = [Bandit(strategy = 'UCB', UCB = ucb) for ucb in UCBs]
best_action_counts,rewards = simulate(runs, time, bandits)
for ucb, rewards in zip(UCBs, rewards):
plt.plot(rewards / time, label='UCB = %.02f' % (ucb))
plt.xlabel('Steps')
plt.ylabel('Average reward')
plt.legend()
plt.savefig('4_UCB_average_reward.png')
plt.close()
for ucb, counts in zip(UCBs, best_action_counts):
plt.plot(counts, label='UCB = %.02f' % (ucb))
plt.xlabel('Steps')
plt.ylabel('% optimal action')
plt.legend()
plt.savefig('5_UCB_best_actions_count.png')
plt.close()
def update_step_size(runs=2000, time=1000):
step_sizes = np.arange(0.05,0.35, step = 0.1)
bandits = [Bandit(update_mode = 'step_size', step_size = step_size) for step_size in step_sizes]
best_action_counts, rewards = simulate(runs, time, bandits)
for step_size, rewards in zip(step_sizes, rewards):
plt.plot(rewards / time, label='step size = %.02f' % (step_size))
plt.xlabel('Steps')
plt.ylabel('Average reward')
plt.legend()
plt.savefig('6_step-size-update_average_reward.png')
plt.close()
for step_size, counts in zip(step_sizes, best_action_counts):
plt.plot(counts, label='step size = %.02f' % (step_size))
plt.xlabel('Steps')
plt.ylabel('% optimal action')
plt.legend()
plt.savefig('7_step-size-update_best_actions_count.png')
plt.close()
def optimistic_evaluation(runs=2000, time=1000):
epsilons = [0, 0.02, 0.1]
bandits = [Bandit(epsilon = eps, initial=5) for eps in epsilons]
best_action_counts, rewards = simulate(runs, time, bandits)
for eps, rewards in zip(epsilons, rewards):
plt.plot(rewards / time, label='epsilon = %.02f, q = 5' % (eps))
plt.xlabel('Steps')
plt.ylabel('Average reward')
plt.legend()
plt.savefig('8_optimistic_evaluation_average_reward.png')
plt.close()
for eps, counts in zip(epsilons, best_action_counts):
plt.plot(counts, label='epsilon = %.02f, q = 5' % (eps))
plt.xlabel('Steps')
plt.ylabel('% optimal action')
plt.legend()
plt.savefig('9_optimistic_evaluation_best_actions_count.png')
plt.close()
def comparison_UCB_epsilon_greedy(runs=2000, time=1000):
bandits = []
bandits.append(Bandit(strategy = 'UCB', UCB=0.6))
bandits.append(Bandit(strategy = 'epsilon-greedy', epsilon=0.1))
best_action_counts, rewards = simulate(runs, time, bandits)
plt.plot(rewards[0] / time, label='UCB c = 0.6')
plt.plot(rewards[1] / time, label='epsilon-greedy epsilon = 0.1')
plt.xlabel('Steps')
plt.ylabel('Average reward')
plt.legend()
plt.savefig('10_comparison_UCB_epsilon-greedy_average_reward.png')
plt.close()
plt.plot(best_action_counts[0], label='UCB c = 0.6')
plt.plot(best_action_counts[1], label='epsilon-greedy epsilon = 0.1')
plt.xlabel('Steps')
plt.ylabel('% optimal action')
plt.legend()
plt.savefig('11_comparison_UCB_epsilon-greedy_best_action.png')
plt.close()
if __name__ == '__main__':
illustration_rewards()
parameter_epsilon()
parameter_UCB()
update_step_size()
optimistic_evaluation()
comparison_UCB_epsilon_greedy()