[R] Upper Confidence Bound.ipynb

Kernel: R

Upper Confidence Bound

A very great 4 minutes video on confidence interval

Data preprocessing

# Importing the dataset
dataset = read.csv('Ads_CTR_Optimisation.csv')

head(dataset, 10)

Implementing the Upper Confidence Bound

N = dim(dataset)[1]
d = dim(dataset)[2]
ads_selected = integer(0)

nb_of_sel = integer(d) # Number of Selections
sum_of_rwd = integer(d) # Sums of reward
total_reward = 0

for (n in 1:N){
    ad = 0
    max_upper_bound = 0
    for(i in 1:d){
        if(nb_of_sel[i] > 0){
            average_reward = sum_of_rwd[i] / nb_of_sel[i]
            delta_i = sqrt(3/2 * log(n) / 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(ads_selected, ad)
    nb_of_sel[ad] = nb_of_sel[ad] + 1
    reward = dataset[n, ad]
    sum_of_rwd[ad] = sum_of_rwd[ad] + reward
    total_reward = total_reward + reward
}

total_reward

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

Visualizing the results

hist(ads_selected, 
     col = 'green', 
     main = 'Histogram of Ads selected',
     xlab = 'Ads',
     ylab = 'Number of time each Ad was selected')