New Mathematical Framework for Bellman Residual Minimization in Reinforcement Learning Control
Researchers have established foundational theoretical results for using Bellman residual minimization to solve control problems in reinforcement learning, an approach that has been less studied than traditional dynamic programming methods. While Bellman residual minimization offers advantages like more stable convergence with function approximation, it has historically been less efficient in practice and harder to apply to model-free settings. This work addresses a gap in the literature by providing rigorous mathematical foundations for applying this method to policy optimization tasks.
A new arXiv preprint presents theoretical advances for Bellman residual minimization applied to control problems in Markov decision processes. The paper establishes foundational results for policy optimization using this approach, which directly minimizes the squared Bellman residual objective function. While dynamic programming remains the most common solution method for such problems, Bellman residual minimization offers potential advantages including more stable convergence when using function approximation for value functions. However, the method has received less research attention due to practical efficiency concerns and difficulties extending it to model-free reinforcement learning settings. This work fills a gap in the literature by providing rigorous mathematical analysis of the method's geometry, stationarity conditions, and convergence properties specifically for control tasks, complementing existing research that has focused primarily on policy evaluation.
What's missing
The paper's specific convergence rates, empirical performance comparisons with dynamic programming methods, and practical applicability to real-world control problems are not detailed in the abstract provided.
What different sources said
- arXiv cs.LGCenter
Bellman Residual Minimization for Control: Geometry, Stationarity, and Convergence
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