Using Localization and Factorization to Reduce the Complexity of Reinforcement Learning

General reinforcement learning is a powerful framework for artificial intelligence that has seen much theoretical progress since introduced fifteen years ago. We have previously provided guarantees for cases with finitely many possible environments. Though the results are the best possible in general, a linear dependence on the size of the hypothesis class renders them impractical. However, we dramatically improved on these by introducing the concept of environments generated by combining laws. The bounds are then linear in the number of laws needed to generate the environment class. This number is identified as a natural complexity measure for classes of environments. The individual law might only predict some feature (factorization) and only in some contexts (localization). We here extend previous deterministic results to the important stochastic setting