Optimal Regret Bounds for Selecting the State Representation in Reinforcement Learning
This addresses the challenge of representation selection in non-Markovian RL for agents in continuous interaction settings, providing a theoretically optimal solution.
The paper tackles the problem of selecting the best state representation in reinforcement learning when the environment is not necessarily Markovian, aiming to minimize regret against an optimal agent. It achieves a regret bound of O(√T), which is optimal and improves upon prior O(T^{2/3}) bounds with smaller constants.
We consider an agent interacting with an environment in a single stream of actions, observations, and rewards, with no reset. This process is not assumed to be a Markov Decision Process (MDP). Rather, the agent has several representations (mapping histories of past interactions to a discrete state space) of the environment with unknown dynamics, only some of which result in an MDP. The goal is to minimize the average regret criterion against an agent who knows an MDP representation giving the highest optimal reward, and acts optimally in it. Recent regret bounds for this setting are of order $O(T^{2/3})$ with an additive term constant yet exponential in some characteristics of the optimal MDP. We propose an algorithm whose regret after $T$ time steps is $O(\sqrt{T})$, with all constants reasonably small. This is optimal in $T$ since $O(\sqrt{T})$ is the optimal regret in the setting of learning in a (single discrete) MDP.