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We consider an agent interacting with an environment in a single stream ofactions, observations, and rewards, with no reset. This process is not assumedto be a Markov Decision Process (MDP). Rather, the agent has severalrepresentations (mapping histories of past interactions to a discrete statespace) of the environment with unknown dynamics, only some of which result inan MDP. The goal is to minimize the average regret criterion against an agentwho knows an MDP representation giving the highest optimal reward, and actsoptimally in it. Recent regret bounds for this setting are of order$O(T^{2/3})$ with an additive term constant yet exponential in somecharacteristics of the optimal MDP. We propose an algorithm whose regret after$T$ time steps is $O(\sqrt{T})$, with all constants reasonably small. This isoptimal in $T$ since $O(\sqrt{T})$ is the optimal regret in the setting oflearning in a (single discrete) MDP.

Optimal Regret Bounds for Selecting the State Representation in Reinforcement Learning