Reinforcement Learning for Infinite-Horizon Average-Reward Linear MDPs via Approximation by Discounted-Reward MDPs

TL;DR

This paper introduces a novel reinforcement learning algorithm for infinite-horizon average-reward linear MDPs that achieves near-optimal regret bounds with polynomial computational complexity without strong assumptions on the dynamics.

Contribution

It proposes the first polynomial-time algorithm that approximates average-reward MDPs via discounted MDPs and achieves $ ilde{O}( oot{T} ull)$ regret without ergodicity assumptions.

Findings

Achieves $ ilde{O}( oot{T} ull)$ regret bound.

Computational complexity polynomial in problem parameters.

Does not require strong assumptions like ergodicity.

Abstract

We study the problem of infinite-horizon average-reward reinforcement learning with linear Markov decision processes (MDPs). The associated Bellman operator of the problem not being a contraction makes the algorithm design challenging. Previous approaches either suffer from computational inefficiency or require strong assumptions on dynamics, such as ergodicity, for achieving a regret bound of $\widetilde{O}(\sqrt{T})$. In this paper, we propose the first algorithm that achieves $\widetilde{O}(\sqrt{T})$ regret with computational complexity polynomial in the problem parameters, without making strong assumptions on dynamics. Our approach approximates the average-reward setting by a discounted MDP with a carefully chosen discounting factor, and then applies an optimistic value iteration. We propose an algorithmic structure that plans for a nonstationary policy through optimistic value iteration and follows that policy until a specified information metric in the collected data doubles. Additionally, we introduce a value function clipping procedure for limiting the span of the value function for sample efficiency.