# Globally Convergent Offline Reinforcement Learning with Smoothed Bellman Residual Minimization

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Text version: https://stenobird.com/podcast/best-ai-papers-explained-7258006/globally-convergent-offline-reinforcement-learning-with-smoothed-bellman-residual-minimization.md
Podcast: [Best AI papers explained](https://stenobird.com/podcast/best-ai-papers-explained-7258006)
Published: 2026-07-13T17:35:57+00:00
Episode link: https://podcasters.spotify.com/pod/show/ehwkang/episodes/Globally-Convergent-Offline-Reinforcement-Learning-with-Smoothed-Bellman-Residual-Minimization-e3m1h8c
Audio file: https://anchor.fm/s/1026675f8/podcast/play/122782412/https%3A%2F%2Fd3ctxlq1ktw2nl.cloudfront.net%2Fstaging%2F2026-6-13%2F427886607-44100-2-ac9a8e06e51b3.m4a
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Duration seconds: 745

## Resource

This paper introduces **Off-GLADIUS**, a novel algorithm designed for **offline reinforcement learning** that utilizes **Bellman Residual Minimization (BRM)**. While traditional BRM methods often struggle with stability and convergence issues, this research proves that the proposed approach achieves **global optimality** by satisfying a **Polyak–Łojasiewicz (PL) condition**. The authors establish that for linear and sufficiently wide **neural networks**, the algorithm converges linearly to the global optimum despite the non-convex nature of the objective function. This theoretical breakthrough addresses a long-standing open question regarding the convergence guarantees of gradient-based BRM in offline settings. Empirically, the study demonstrates that **Off-GLADIUS** matches or exceeds the performance of established baselines like **Conservative Q-Learning (CQL)** and **OptiDICE** across various control benchmarks. Ultimately, the paper bridges the gap between theoretical stability and practical effectiveness, offering a rigorous framework for learning optimal policies from fixed datasets.

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