Structured Best Arm Identification with Fixed Confidence
Proceedings of the 28th International Conference on Algorithmic Learning Theory, PMLR 76:593-616, 2017.
We study the problem of identifying the best action among a set of possible options when the value of each action is given by a mapping from a number of noisy micro-observables in the so-called fixed confidence setting. Our main motivation is the application to minimax game search, which has been a major topic of interest in artificial intelligence. In this paper we introduce an abstract setting to clearly describe the essential properties of the problem. While previous work only considered a two-move-deep game tree search problem, our abstract setting can be applied to the general minimax games where the depth can be non-uniform and arbitrary, and transpositions are allowed. We introduce a new algorithm (LUCB-micro) for the abstract setting, and give its lower and upper sample complexity results. Our bounds recover some previous results, achieved in more limited settings, and also shed further light on how the structure of minimax problems influences sample complexity.