forked from yang0110/graph-based-bandit
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adaptive_lapucb.py
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adaptive_lapucb.py
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'''
Only approximate M_T for items selection
keep the exact estimation
'''
import numpy as np
from sklearn.metrics.pairwise import rbf_kernel
from sklearn.preprocessing import Normalizer, MinMaxScaler
from scipy.sparse import csgraph
import scipy
import os
class LAPUCB_ADAP():
def __init__(self, dimension, user_num, item_num, pool_size, item_feature_matrix, true_user_feature_matrix, true_payoffs, noise_matrix, normed_lap, alpha, delta, sigma):
self.dimension=dimension
self.user_num=user_num
self.item_num=item_num
self.pool_size=pool_size
self.item_feature_matrix=item_feature_matrix
self.true_user_feature_matrix=true_user_feature_matrix
self.true_payoffs=true_payoffs
self.noise_matrix=noise_matrix
self.user_feature_matrix=np.zeros((self.user_num, self.dimension))
self.L=normed_lap+0.01*np.identity(self.user_num)
self.true_L=normed_lap
self.A=np.kron(self.L, np.identity(self.dimension))
self.A_inv=np.linalg.pinv(self.A)
self.alpha=alpha
self.delta=delta
self.sigma=sigma
self.beta=0
self.user_cov={}
self.user_old_cov={}
self.cov=self.alpha*self.A
self.cov_inv=np.linalg.pinv(self.cov)
self.user_phi={}
self.bias=np.zeros((self.user_num*self.dimension))
self.beta_list=[]
self.a_list=[]
self.b_list=[]
self.c_list=[]
self.M_ii_list=[]
self.M_inv_ij_list=[]
self.bias_ij_list=[]
self.z={}
self.cov_inv_sub={}
def initialized_parameter(self):
for u in range(self.user_num):
self.user_cov[u]=np.zeros((self.dimension, self.dimension))
self.user_phi[u]=np.zeros((self.dimension, self.dimension))
self.user_old_cov[u]=np.zeros((self.dimension, self.dimension))
self.z[u]=np.zeros(self.dimension)
self.cov_inv_sub[u]=np.zeros((self.dimension, self.user_num*self.dimension))
# def update_beta(self, user_index):
# a=np.linalg.det(self.user_cov[user_index])**(1/2)
# b=np.linalg.det(self.user_phi[user_index])**(-1/2)
# d=self.sigma*np.sqrt(2*np.log(a*b/self.delta))
# theta=self.true_user_feature_matrix[user_index]
# dot=np.dot(self.user_phi[user_index], theta)
# dot_norm=np.linalg.norm(dot)
# c=np.sqrt(1/(self.alpha))*dot_norm
# cov_inv=np.linalg.pinv(self.user_cov[user_index])
# norm=np.sqrt(np.dot(np.dot(dot, cov_inv), dot))
# self.beta=c+d
# self.beta_list.extend([self.beta])
# self.d_list.extend([d])
# self.c_list.extend([c])
def true_beta(self, user_index):
M_inv_sub=self.cov_inv[user_index*self.dimension:(user_index+1)*self.dimension].copy()
M_ii=self.user_cov[user_index]
M_inv_ii=np.linalg.pinv(M_ii)
phi_ii=self.user_phi[user_index]
z=self.z[user_index]
true_theta=self.true_user_feature_matrix[user_index]
est_theta=self.user_feature_matrix[user_index]
a=-np.dot(phi_ii, est_theta)
b=z
c=np.zeros(self.dimension)
for u in range(self.user_num):
if u==user_index:
pass
else:
M_inv_ij=M_inv_sub[:,u*self.dimension:(u+1)*self.dimension]
bias_ij=self.bias[u*self.dimension:(u+1)*self.dimension]
c+=np.dot(np.dot(M_ii, M_inv_ij), bias_ij)
total=a+b+c
self.beta=np.sqrt(np.dot(np.dot(total, M_inv_ii), total))
self.beta_list.extend([self.beta])
self.a_list.extend([np.linalg.norm(a)])
self.b_list.extend([np.linalg.norm(b)])
self.c_list.extend([np.linalg.norm(c)])
self.M_ii_list.extend([np.linalg.norm(M_ii)])
self.M_inv_ij_list.extend([np.linalg.norm(M_inv_ij)])
self.bias_ij_list.extend([np.linalg.norm(bias_ij)])
def select_item(self, item_pool, user_index, time):
item_fs=self.item_feature_matrix[item_pool]
estimated_payoffs=np.zeros(self.pool_size)
self.true_beta(user_index)
cov_inv=np.linalg.pinv(self.user_cov[user_index])
for j in range(self.pool_size):
x=item_fs[j]
x_norm=np.sqrt(np.dot(np.dot(x, cov_inv),x))
est_y=np.dot(x, self.user_feature_matrix[user_index])+self.beta*x_norm
estimated_payoffs[j]=est_y
max_index=np.argmax(estimated_payoffs)
selected_item_index=item_pool[max_index]
selected_item_feature=item_fs[max_index]
true_payoff=self.true_payoffs[user_index, selected_item_index]
max_ideal_payoff=np.max(self.true_payoffs[user_index][item_pool])
regret=max_ideal_payoff-true_payoff
self.z[user_index]+=selected_item_feature*self.noise_matrix[user_index,selected_item_index]
return true_payoff, selected_item_feature, regret
def update_user_feature(self, true_payoff, selected_item_feature, user_index):
self.user_old_cov[user_index]+=np.outer(selected_item_feature, selected_item_feature)
x_long=np.zeros((self.user_num*self.dimension))
x_long[user_index*self.dimension:(user_index+1)*self.dimension]=selected_item_feature
self.cov+=np.outer(x_long, x_long)
self.bias+=true_payoff*x_long
self.cov_inv=np.linalg.pinv(self.cov)
self.user_feature_matrix=np.dot(self.cov_inv, self.bias).reshape((self.user_num, self.dimension))
self.user_cov[user_index]=np.linalg.pinv(self.cov_inv[user_index*self.dimension:(user_index+1)*self.dimension,user_index*self.dimension:(user_index+1)*self.dimension])
self.user_phi[user_index]=self.user_cov[user_index]-self.user_old_cov[user_index]
def update_graph(self):
adj=rbf_kernel(self.user_feature_matrix)
self.L=csgraph.laplacian(adj, normed=True)
A_t_1=self.A.copy()
self.A=np.kron(self.L+0.01*np.identity(self.user_num), np.identity(self.dimension))
self.cov+=self.alpha*(self.A-A_t_1)
def run(self, user_array, item_pool_array, iteration):
self.initialized_parameter()
cumulative_regret=[0]
learning_error_list=np.zeros(iteration)
graph_learning_error=np.zeros(iteration)
for time in range(iteration):
print('time/iteration', time, iteration,'~~~LAPUCB ADAP')
user_index=user_array[time]
item_pool=item_pool_array[time]
true_payoff, selected_item_feature, regret=self.select_item(item_pool,user_index, time)
self.update_user_feature(true_payoff, selected_item_feature, user_index)
self.update_graph()
error=np.linalg.norm(self.user_feature_matrix-self.true_user_feature_matrix)
cumulative_regret.extend([cumulative_regret[-1]+regret])
learning_error_list[time]=error
graph_learning_error[time]=np.linalg.norm(self.L-self.true_L)
return np.array(cumulative_regret), learning_error_list, graph_learning_error, self.beta_list, self.a_list, self.b_list, self.c_list, self.M_ii_list,self.M_inv_ij_list,self.bias_ij_list