Narrowing the Gap between Adversarial and Stochastic MDPs via Policy Optimization - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2024

Narrowing the Gap between Adversarial and Stochastic MDPs via Policy Optimization

Abstract

In this paper, we consider the problem of learning in adversarial Markov decision processes [MDPs] with an oblivious adversary in a full-information setting. The agent interacts with an environment during $T$ episodes, each of which consists of $H$ stages, and each episode is evaluated with respect to a reward function that will be revealed only at the end of the episode. We propose an algorithm, called APO-MVP, that achieves a regret bound of order $\tilde{\mathcal{O}}(\mathrm{poly}(H)\sqrt{SAT})$, where $S$ and $A$ are sizes of the state and action spaces, respectively. This result improves upon the best-known regret bound by a factor of $\sqrt{S}$, bridging the gap between adversarial and stochastic MDPs, and matching the minimax lower bound $\Omega(\sqrt{H^3SAT})$ as far as the dependencies in $S,A,T$ are concerned. The proposed algorithm and analysis completely avoid the typical tool given by occupancy measures; instead, it performs policy optimization based only on dynamic programming and on a black-box online linear optimization strategy run over estimated advantage functions, making it easy to implement. The analysis leverages two recent techniques: policy optimization based on online linear optimization strategies (Jonckheere et al., 2023) and a refined martingale analysis of the impact on values of estimating transitions kernels (Zhang et al., 2023).
Fichier principal
Vignette du fichier
TCS--RL-dependency-S.pdf (345.9 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04636422 , version 1 (05-07-2024)

Identifiers

  • HAL Id : hal-04636422 , version 1

Cite

Daniil Tiapkin, Evgenii Chzhen, Gilles Stoltz. Narrowing the Gap between Adversarial and Stochastic MDPs via Policy Optimization. 2024. ⟨hal-04636422⟩
0 View
0 Download

Share

Gmail Mastodon Facebook X LinkedIn More