We consider a generalization of stochastic bandit problems where the set of arms, X<\/i>, is allowed to be a generic topological space and the mean-payoff function is \u201clocally Lipschitz\u201d with respect to a dissimilarity function that is known to the decision maker. Under this condition we construct an arm selection policy whose regret improves upon previous results for a large class of problems. In particular, our results imply that if\u00a0X\u00a0<\/i>is the unit hypercube in a Euclidean space and the mean-payoff function has a \ufb01nite number of global maxima around which the behavior of the function is locally H\u00f6lder with a known exponent, then the expected regret is bounded up to a logarithmic factor by \u221a<\/i>n, i.e., the rate of\u00a0the growth of the regret is independent of the dimension of the space. Moreover, we prove the minimax optimality of our algorithm for the class of mean-payoff functions we consider.<\/p>\n","protected":false},"excerpt":{"rendered":"
We consider a generalization of stochastic bandit problems where the set of arms, X, is allowed to be a generic topological space and the mean-payoff function is \u201clocally Lipschitz\u201d with respect to a dissimilarity function that is known to the decision maker. 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