Minimax Lower Bounds for the Two-Armed Bandit Problem
نویسنده
چکیده
We obtain minimax lower bounds on the regret for the classical two-armed bandit problem. We provide a nite-sample minimax version of the well-known log n asymptotic lower bound of Lai and Robbins. Also, in contrast to the logn asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable con gurations of the two arms. That is, we show that for every allocation rule and for every n, there is a con guration such that the regret at time n is at least 1 times the regret of random guessing, where is any small positive constant. This work was supported in part by the National Science Foundation under NYI grant IRI-9457645.
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