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Convergence Analysis of Reinforcement Learning Algorithms Using Generalized Weak Contraction Mappings

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Publikašuvnnas:Symmetry vol. 17, no. 5 (2025), p. 750
Váldodahkki: Belhenniche Abdelkader
Eará dahkkit: Chertovskih Roman, Gonçalves Rui
Almmustuhtton:
MDPI AG
Fáttát:
Mathematical functions
Iterative algorithms
Dynamic programming
Convergence
Algorithms
Machine learning
Iterative methods
Feedback control
Fixed points (mathematics)
Optimization
Decision making
Markov analysis
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Abstrákta:We investigate the convergence properties of policy iteration and value iteration algorithms in reinforcement learning by leveraging fixed-point theory, with a focus on mappings that exhibit weak contractive behavior. Unlike traditional studies that rely on strong contraction properties, such as those defined by the Banach contraction principle, we consider a more general class of mappings that includes weak contractions. Employing Zamfirscu’s fixed-point theorem, we establish sufficient conditions for norm convergence in infinite-dimensional policy spaces under broad assumptions. Our approach extends the applicability of these algorithms to feedback control problems in reinforcement learning, where standard contraction conditions may not hold. Through illustrative examples, we demonstrate that this framework encompasses a wider range of operators, offering new insights into the robustness and flexibility of iterative methods in dynamic programming.
ISSN:2073-8994
DOI:10.3390/sym17050750
Gáldu:Engineering Database