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import numpy as np
import matplotlib.pyplot as plt
import math
number_of_bandits=10
number_of_arms=10
number_of_pulls=10000
epsilon=0.3
min_temp = 0.1
decay_rate=0.999def pick_arm(q_values,counts,strategy,success,failure):global epsilonif strategy=="random":return np.random.randint(0,len(q_values))if strategy=="greedy":best_arms_value = np.max(q_values)best_arms = np.argwhere(q_values==best_arms_value).flatten()return best_arms[np.random.randint(0,len(best_arms))]if strategy=="egreedy" or strategy=="egreedy_decay": if  strategy=="egreedy_decay": epsilon=max(epsilon*decay_rate,min_temp)if np.random.random() > epsilon:best_arms_value = np.max(q_values)best_arms = np.argwhere(q_values==best_arms_value).flatten()return best_arms[np.random.randint(0,len(best_arms))]else:return np.random.randint(0,len(q_values))if strategy=="ucb":total_counts = np.sum(counts)q_values_ucb = q_values + np.sqrt(np.reciprocal(counts+0.001)*2*math.log(total_counts+1.0))best_arms_value = np.max(q_values_ucb)best_arms = np.argwhere(q_values_ucb==best_arms_value).flatten()return best_arms[np.random.randint(0,len(best_arms))]if strategy=="thompson":sample_means = np.zeros(len(counts))for i in range(len(counts)):sample_means[i]=np.random.beta(success[i]+1,failure[i]+1)return np.argmax(sample_means)fig = plt.figure()
ax = fig.add_subplot(111)
for st in ["greedy","random","egreedy","egreedy_decay","ucb","thompson"]:best_arm_counts = np.zeros((number_of_bandits,number_of_pulls))for i in range(number_of_bandits):arm_means = np.random.rand(number_of_arms)best_arm = np.argmax(arm_means)q_values = np.zeros(number_of_arms)counts = np.zeros(number_of_arms)success=np.zeros(number_of_arms)failure=np.zeros(number_of_arms)for j in range(number_of_pulls):a = pick_arm(q_values,counts,st,success,failure)reward = np.random.binomial(1,arm_means[a])counts[a]+=1.0q_values[a]+= (reward-q_values[a])/counts[a]success[a]+=rewardfailure[a]+=(1-reward)best_arm_counts[i][j] = counts[best_arm]*100.0/(j+1)epsilon=0.3ys = np.mean(best_arm_counts,axis=0)xs = range(len(ys))ax.plot(xs, ys,label = st)plt.xlabel('Steps')
plt.ylabel('Optimal pulls')plt.tight_layout()
plt.legend()
plt.ylim((0,110))
plt.show()        ##################

相关代码：

# -*- coding: utf-8 -*-
import numpy as np
from matplotlib import pylab as plt
#from mpltools import style # uncomment for prettier plots
#style.use(['ggplot'])'''
function definitions
'''
# generate all bernoulli rewards ahead of time
def generate_bernoulli_bandit_data(num_samples,K):CTRs_that_generated_data = np.tile(np.random.rand(K),(num_samples,1))true_rewards = np.random.rand(num_samples,K) < CTRs_that_generated_datareturn true_rewards,CTRs_that_generated_data# totally random
def random(estimated_beta_params):return np.random.randint(0,len(estimated_beta_params))# the naive algorithm
def naive(estimated_beta_params,number_to_explore=100):totals = estimated_beta_params.sum(1) # totalsif np.any(totals < number_to_explore): # if have been explored less than specifiedleast_explored = np.argmin(totals) # return the one least exploredreturn least_exploredelse: # return the best mean foreversuccesses = estimated_beta_params[:,0] # successesestimated_means = successes/totals # the current meansbest_mean = np.argmax(estimated_means) # the best meanreturn best_mean# the epsilon greedy algorithm
def epsilon_greedy(estimated_beta_params,epsilon=0.01):totals = estimated_beta_params.sum(1) # totalssuccesses = estimated_beta_params[:,0] # successesestimated_means = successes/totals # the current meansbest_mean = np.argmax(estimated_means) # the best meanbe_exporatory = np.random.rand() < epsilon # should we explore?if be_exporatory: # totally random, excluding the best_meanother_choice = np.random.randint(0,len(estimated_beta_params))while other_choice == best_mean:other_choice = np.random.randint(0,len(estimated_beta_params))return other_choiceelse: # take the best meanreturn best_mean# the UCB algorithm using
# (1 - 1/t) confidence interval using Chernoff-Hoeffding bound)
# for details of this particular confidence bound, see the UCB1-TUNED section, slide 18, of:
# http://lane.compbio.cmu.edu/courses/slides_ucb.pdf
def UCB(estimated_beta_params):t = float(estimated_beta_params.sum()) # total number of rounds so fartotals = estimated_beta_params.sum(1)successes = estimated_beta_params[:,0]estimated_means = successes/totals # sample meanestimated_variances = estimated_means - estimated_means**2    UCB = estimated_means + np.sqrt( np.minimum( estimated_variances + np.sqrt(2*np.log(t)/totals), 0.25 ) * np.log(t)/totals )return np.argmax(UCB)# the UCB algorithm - using fixed 95% confidence intervals
# see slide 8 for details:
# http://dept.stat.lsa.umich.edu/~kshedden/Courses/Stat485/Notes/binomial_confidence_intervals.pdf
def UCB_bernoulli(estimated_beta_params):totals = estimated_beta_params.sum(1) # totalssuccesses = estimated_beta_params[:,0] # successesestimated_means = successes/totals # sample meanestimated_variances = estimated_means - estimated_means**2UCB = estimated_means + 1.96*np.sqrt(estimated_variances/totals)return np.argmax(UCB)# the bandit algorithm
def run_bandit_dynamic_alg(true_rewards,CTRs_that_generated_data,choice_func):num_samples,K = true_rewards.shape# seed the estimated params (to avoid )prior_a = 1. # aka successes prior_b = 1. # aka failuresestimated_beta_params = np.zeros((K,2))estimated_beta_params[:,0] += prior_a # allocating the initial conditionsestimated_beta_params[:,1] += prior_bregret = np.zeros(num_samples) # one for each of the 3 algorithmsfor i in range(0,num_samples):# pulling a lever & updating estimated_beta_paramsthis_choice = choice_func(estimated_beta_params)# update parametersif true_rewards[i,this_choice] == 1:update_ind = 0else:update_ind = 1estimated_beta_params[this_choice,update_ind] += 1# updated expected regretregret[i] = np.max(CTRs_that_generated_data[i,:]) - CTRs_that_generated_data[i,this_choice]cum_regret = np.cumsum(regret)return cum_regretif __name__ == '__main__':'''main code'''# define number of samples and number of choicesnum_samples = 10000K = 5 # number of armsnumber_experiments = 100regret_accumulator = np.zeros((num_samples,5))for i in range(number_experiments):print "Running experiment:", i+1true_rewards,CTRs_that_generated_data = generate_bernoulli_bandit_data(num_samples,K)regret_accumulator[:,0] += run_bandit_dynamic_alg(true_rewards,CTRs_that_generated_data,random)regret_accumulator[:,1] += run_bandit_dynamic_alg(true_rewards,CTRs_that_generated_data,naive)regret_accumulator[:,2] += run_bandit_dynamic_alg(true_rewards,CTRs_that_generated_data,epsilon_greedy)regret_accumulator[:,3] += run_bandit_dynamic_alg(true_rewards,CTRs_that_generated_data,UCB)regret_accumulator[:,4] += run_bandit_dynamic_alg(true_rewards,CTRs_that_generated_data,UCB_bernoulli)plt.semilogy(regret_accumulator/number_experiments)plt.title('Simulated Bandit Performance for K = 5')plt.ylabel('Cumulative Expected Regret')plt.xlabel('Round Index')plt.legend(('Random','Naive','Epsilon-Greedy','(1 - 1/t) UCB','95% UCB'),loc='lower right')plt.show()

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