- Abstract: We study efficient algorithms for reinforcement learning in Markov decision processes, whose complexity is independent of the number of states. This formulation succinctly captures large scale problems, but is also known to be computationally hard in its general form. Previous approaches attempt to circumvent the computational hardness by assuming structure in either transition function or the value function, or by relaxing the solution guarantee to a local optimality condition. We consider the methodology of boosting, borrowed from supervised learning, for converting weak learners into an effective policy. The notion of weak learning we study is that of sampled-based approximate optimization of linear functions over policies. Under this assumption of weak learnability, we give an efficient algorithm that is capable of improving the accuracy of such weak learning methods iteratively. We prove sample complexity and running time bounds on our method, that are polynomial in the natural parameters of the problem: approximation guarantee, discount factor, distribution mismatch and number of actions. In particular, our bound does not explicitly depend on the number of states. A technical difficulty in applying previous boosting results, is that the value function over policy space is not convex. We show how to use a non-convex variant of the Frank-Wolfe method, coupled with recent advances in gradient boosting that allow incorporating a weak learner with multiplicative approximation guarantee, to overcome the non-convexity and attain global optimality guarantees.
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