New Study Explores Control Bellman Residual Minimization for Policy Optimization in Markov Decision Problems

Global: New Study Explores Control Bellman Residual Minimization for Policy Optimization in Markov Decision Problems

Researchers Donghwan Lee and Hyukjun Yang submitted a paper to arXiv on January 26, 2026, that establishes foundational results for using control Bellman residual minimization to optimize policies in Markov decision problems (MDPs). The work seeks to fill a gap in the literature where Bellman residual methods have been primarily applied to policy evaluation rather than control tasks.

Background on Markov Decision Problems

Markov decision problems are a standard framework for sequential decision making under uncertainty. Traditionally, dynamic programming techniques such as value iteration and policy iteration have dominated the solution landscape because of their theoretical guarantees and practical performance.

Bellman Residual Minimization

Bellman residual minimization offers an alternative by directly minimizing the squared Bellman residual, a measure of inconsistency between a candidate value function and the Bellman equation. While this approach can be less efficient in some settings, it provides more stable convergence when function approximation is employed, a property that is valuable for large‑scale or model‑free reinforcement learning.

Gap in Existing Research

Prior investigations have largely focused on Bellman residual methods for policy evaluation, leaving the control aspect—where the objective is to improve the policy itself—relatively underexplored. The authors note that this limitation has constrained the broader adoption of residual‑based techniques in reinforcement learning pipelines.

Contributions of the Paper

The study introduces theoretical guarantees for control Bellman residual minimization, outlining conditions under which the method converges to an optimal or near‑optimal policy. It also proposes algorithmic adaptations that make the approach compatible with common function approximators such as neural networks.

Implications for Reinforcement Learning

If the proposed methods prove effective in empirical evaluations, they could offer a more robust alternative to classic dynamic programming in settings where exact models are unavailable. The authors suggest that the technique may reduce variance in policy updates and improve sample efficiency, although further experimental validation is required.

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.