![]() Values: Represent the known mean reward.Counts: Represent recorded times when arm was pulled. RETURN OF THE TIME BANDIT CODEFor further understanding of the code, I have included comments for easier understanding.īelow is the code for creation of the UCB1 algorithm setup and progressive updates of counts and values for arms. The following analysis is based on the book “Bandit Algorithms for Website Optimization” by John Myles White. Depending on its current average mean, the overall UCB function representation of that specific arm may be greater than other arms with higher return but smaller components, and consequently enable that arm to be picked. Thus, an arm that has not been explored as often as other arms will have a bigger UCB component. For any increase in n, the UCB increases only by logarithmic time, while for any increase in n_i, the UCB decreases by n_i. The time complexity between the numerator and denominator provides a tension between exploration and exploitation. Thereafter, the UCB algorithm always picks the arm with the highest reward UCB as represented by the equation above.īeyond the formulation explanation, here is a simple thought experiment to glean some intuition on how UCB algorithm incorporates exploration and exploitation. The more times the specific arm has been engaged before in the past, the greater the confidence boundary reduces towards the point estimate. This upper boundary is inversely proportional to the squared root of n_i.The upper boundary is proportional to the squared root of ln(n), which means that when the experiment progresses, all arms have their upper boundaries increases by a factor of squared root of ln(n).The above formulation is simple but yet has several interesting implications as explained in the following: Where mu_i represents the current reward return average of arm i at the current round, n represents the number of trials passed, and n_i represents the number of pulls given to arm i in the playthrough history. ![]()
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