[Python] Upper Confidence Bound.ipynb

Kernel: Python 3

Upper Confidence Bound

A very great 4 minutes video on confidence interval

Data preprocessing

# Importing the libraries
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import math
%matplotlib inline
plt.rcParams['figure.figsize'] = [14, 8]

dataset = pd.read_csv('Ads_CTR_Optimisation.csv')

dataset.head(10)

Implementing the Upper Confidence Bound

N = len(dataset)
d = len(dataset.iloc[0].values)
ads_selected = []

nb_of_sel = [0] * d # Number of Selections
sum_of_rwd = [0] * d # Sums of reward
total_reward = 0

for n in range(0, N):
    ad = 0
    max_upper_bound = 0
    for i in range(0, d):
        if nb_of_sel[i] > 0:
            average_reward = sum_of_rwd[i] / nb_of_sel[i]
            delta_i = math.sqrt(3/2 * math.log(n+1) / nb_of_sel[i])
            upper_bound = average_reward + delta_i
        else:
            upper_bound = 1e400
            
        if upper_bound > max_upper_bound:
            max_upper_bound = upper_bound
            ad = i
    ads_selected.append(ad)
    nb_of_sel[ad] += 1
    reward = dataset.values[n, ad]
    sum_of_rwd[ad] += reward
    total_reward = total_reward + reward

total_reward

2178

# Best ad having highest convergent rate can be found by checking last few data of ads_selected
ads_selected[9980:10000]

[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]

Visualizing the results

plt.hist(ads_selected)
plt.title('Histogram of Ads selected')
plt.xlabel('Ads')
plt.ylabel('Number of time each Ad was selected')

Text(0,0.5,'Number of time each Ad was selected')