Study Provides O(1/n) Stability Bounds for Offline Reinforcement Learning

Global: Study Provides O(1/n) Stability Bounds for Offline Reinforcement Learning

A new study posted on arXiv on January 23, 2026, presents theoretical advances for offline reinforcement learning and offline inverse reinforcement learning. The paper, authored by Enoch H. Kang and Kyoungseok Jang, introduces a statistical framework that yields O(1/n) on‑average argument‑stability and excess‑risk bounds for Bellman residual minimization.

Background

Offline reinforcement learning seeks to derive near‑optimal value functions from a fixed dataset of logged trajectories, while offline inverse reinforcement learning aims to recover underlying reward models. Existing approaches often struggle to enforce Bellman consistency, a key condition for optimality.

Methodology

The authors focus on Bellman residual minimization (BRM) and build on a recently discovered globally convergent stochastic gradient descent‑ascent (SGDA) algorithm. Their analysis introduces a single Lyapunov potential that couples SGDA runs on neighboring datasets, enabling a unified stability argument.

Theoretical Findings

Using the Lyapunov construction, the study derives an O(1/n) on‑average argument‑stability bound, effectively doubling the best known sample‑complexity exponent for convex‑concave saddle‑point problems. The same stability constant directly translates into an O(1/n) excess‑risk bound for BRM, achieved without variance‑reduction techniques, additional regularization, or restrictive independence assumptions on minibatch sampling.

Practical Implications

The results hold for standard neural‑network parameterizations and minibatch stochastic gradient descent, suggesting that the theoretical guarantees are applicable to contemporary deep‑learning pipelines used in offline RL settings.

Publication Details

The manuscript was originally submitted on August 26, 2025, and revised on January 23, 2026. It is listed under the Machine Learning category (cs.LG) on arXiv and assigned the identifier arXiv:2508.18741.

Outlook

By establishing tighter stability and generalization bounds, the work may influence future algorithmic designs for offline reinforcement learning, potentially improving reliability when learning from fixed datasets.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.