X-Armed Bandits

We consider a generalization of stochastic bandit problems where the set of arms, X, is allowed to be a generic topological space. We constraint the mean-payoff function with a dissimilarity function over X in a way that is more general than Lipschitz. We construct an arm selection policy whose regret improves upon previous result for a large class of problems. In particular, our results imply that if X is the unit hypercube in a Euclidean space and the mean-payoff function has a finite number of global maxima around which the behavior of the function is locally H

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Sébastien Bubeck, Rémi Munos, Gilles Stoltz, Csaba Szepesvári
• Keywords: CORR 2010, Education, Generic Topological Space, Mean-payoff Functions, Stochastic Bandit Problems