Regret Bounds for Learning State Representations in Reinforcement Learning

Abstract

We consider the problem of online reinforcement learning when several state representations (mapping histories to a discrete state space) are available to the learning agent. At least one of these representations is assumed to induce a Markov decision process (MDP), and the performance of the agent is measured in terms of cumulative regret against the optimal policy giving the highest average reward in this MDP representation. We propose an algorithm (UCB-MS) with Õ(√T) regret in any communicating MDP. The regret bound shows that UCB-MS automatically adapts to the Markov model and improves over the currently known best bound of order Õ(T^2/3).