Optimal Regret Bounds for Selecting the State Representation in Reinforcement Learning

TL;DR

This paper introduces an algorithm that achieves optimal $O( oot T)$ regret bounds for selecting the best state representation in reinforcement learning without assuming the environment is an MDP, improving over previous bounds.

Contribution

The paper presents a new algorithm that attains optimal regret bounds for state representation selection in non-MDP environments, with constants that are reasonably small.

Findings

Achieves $O( oot T)$ regret bound, matching the optimal in MDPs.

Outperforms previous $O(T^{2/3})$ regret bounds with large constants.

Provides a practical algorithm with small constants for complex environments.

Abstract

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.