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def calculate_upper_bound(wins, num_selections, n): | |
average_reward = wins / num_selections | |
delta_i = math.sqrt(3/2 * math.log(n + 1) / num_selections) | |
upper_bound = average_reward + delta_i | |
return upper_bound | |
import math | |
import random | |
# Array to store which ads got shown | |
ads_selected = [] | |
# Number of selections for each ad | |
number_of_selections_of_ad = [0] * d | |
# Number of times each ad got clicked | |
number_of_wins = [0] * d | |
total_reward = 0 | |
# For each user | |
for n in range(0, N): | |
selected_ad = 0 | |
max_upper_bound = 0 | |
# Iterate over ads | |
for i in range(0, d): | |
# If ad has been selected atleast once | |
if(number_of_selections_of_ad[i] > 0): | |
# Calculating upper bound of distribution | |
upper_bound = calculate_upper_bound(number_of_wins[i], number_of_selections_of_ad[i], n) | |
# If ad has never been selected | |
else: | |
# Setting upper bound to be a very large number | |
upper_bound = 1e10 | |
if upper_bound > max_upper_bound: | |
max_upper_bound = upper_bound | |
selected_ad = i | |
# Selecting the ad with the highest upper bound, and increasing its no. of selections | |
ads_selected.append(selected_ad) | |
number_of_selections_of_ad[selected_ad] = number_of_selections_of_ad[selected_ad] + 1 | |
# Checking if the ad was clicked | |
reward = df.values[n, selected_ad] | |
if reward == 1: | |
number_of_wins[selected_ad] = number_of_wins[selected_ad] + 1 | |
total_reward = total_reward + reward |
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