In this question, we consider bandit instances in which the number of arms n = 10; assume the set of arms is A = {0, 1, 2, ..., 9}. blob:https://admin.solutioninn.com/204a1237-aaa3-4892-8768-e0979f885823Each arm yields rewards from a Bernoulli distribution whose mean is strictly less than 1. Call this set of bandit instances I. Now consider a family of algorithms L that operate on I, wherein each algorithm L L satisfies the following properties. L is deterministic. In the first n pulls made by L (on steps 0 tn-1), each arm is pulled exactly once. For t = n, n + 1, n + 2,...: if t is not a prime number, then the arm pulled by L on the t-th step has the highest empirical mean among all the arms at that step. In other words, each L E L is a deterministic algorithm that begins with round-robin sampling for n pulls, and thereafter exploits on every step t that is not a prime number. You can assume ties are broken arbitrarily. The chief difference between the elements of L arises from the decisions they make on steps t that are prime numbers there is no restriction on the choice made on such steps. a. Show that there exists Lgood EL such that Lgood achieves sub-linear regret on all I = I. a. Show that there exists Lbad E L such that Lbad does not achieve sub-linear regret on all I EI. Your arguments can be informal: no need for the dense notation of Class Note 1. You can use the fact that the number of prime numbers smaller than any natural number N is (log(N))