4 How to Gamble With Little Regret Suppose that you are gambling at a casino. Every day you play at a slot machine, and your goal is to minimize your losses. We model this as the experts problem. Every day you must take the advice of one of 11. experts (Le. a slot machine). At the end of each day t, if you take advice from expert i, the advice costs you some (:3 in [0,1]. You want to minimize the regret R, dened as: T RZHZ \"am lee, _, a?) where aft) is the expert you choose on day t. Your strategy will be probabilities where p: denotes the probability with which you choose expert 22 on day t. Assume an all powerful adversary (i.e. the casino) can look at your strategy ahead of time and decide the costs associated with each expert on each day. Let 0' denote the set of costs for all experts and all days. Compute maxCUEERD, or the maximum possible (expected) regret that the adversary can guarantee, for each of the following strategies. (a) Choose expert I at every step, i.e. p'i = 1 for all t. (b) Any deterministic strategy, i.e. for each t, there exists some i such that p: = l. (c) Always choose an expert according to some xed probability distribution at every time step. That is, x some 101, . . . ,1)\