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