We show complexity bounds for noisy optimization, in frameworks in which noise is stronger than in previously published papers[19]. We also propose an algorithm based on bandits (variants of [16]) that reaches the bound within logarithmic factors. We emphasize the differences with empirical derived published algorithms.

Abstract. This paper focuses on Active Learning with a limited number of queries; in application domains such as Numerical Engineering, the size of the training set might be limited to a few dozen or hundred examples due to computational constraints. Active Learning under bounded resources is formalized as a finite horizon Reinforcement Learning problem, where the sampling strategy aims at minimizing the expectation of the generalization error. A tractable approximation of the optimal (intractable) policy is presented, the Bandit-based Active Learner (BAAL) algorithm. Viewing Active Learning as a single-player game, BAAL combines UCT, the tree structured multi-armed bandit algorithm proposed by Kocsis and Szepesvári (2006), and billiard algorithms. A proof of principle of the approach demonstrates its good empirical convergence toward an optimal policy and its ability to incorporate prior AL criteria. Its hybridization with the Query-by-Committee approach is found to improve on both stand-alone BAAL and stand-alone QbC.