We study bandit model selection in stochastic environments. Our approach relies on a meta-algorithm that selects between candidate base algorithms. We develop a meta-algorithm-base algorithm abstraction that can work with general classes of base algorithms and different type of adversarial meta-algorithms. Our methods rely on a novel and generic smoothing transformation for bandit algorithms that permits us to obtain optimal $O(\sqrt{T})$ model selection guarantees for stochastic contextual bandit problems as long as the optimal base algorithm satisfies a high probability regret guarantee. We show through a lower bound that even when one of the base algorithms has $O(\log T)$ regret, in general it is impossible to get better than $\Omega(\sqrt{T})$ regret in model selection, even asymptotically. Using our techniques, we address model selection in a variety of problems such as misspecified linear contextual bandits, linear bandit with unknown dimension and reinforcement learning with unknown feature maps. Our algorithm requires the knowledge of the optimal base regret to adjust the meta-algorithm learning rate. We show that without such prior knowledge any meta-algorithm can suffer a regret larger than the optimal base regret.

翻译：我们在随机环境中研究土匪模式选择。 我们的方法依赖于在候选基本算法之间选择的元值算法。 我们开发了一种元- 等- 等- 等- 等- 等- 等- 等( 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等。 我们开发了一个元- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等( 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等- 等 等- 等- 等- 等- 等-