Résumé : Model-based Bayesian Reinforcement Learning (BRL) allows a sound formalization of the problem of acting optimally while facing an unknown environment, i.e., avoiding the exploration-exploitation dilemma. However, algorithms explicitly addressing BRL suffer from such a combinatorial explosion that a large body of work relies on heuristic algorithms. This paper introduces bolt, a simple and (almost) deterministic heuristic algorithm for BRL which is optimistic about the transition function. We analyze bolt's sample complexity, and show that under certain parameters, the algorithm is near-optimal in the Bayesian sense with high probability. Then, experimental results highlight the key differences of this method compared to previous work.