Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees

Abstract:We introduce a principled learning to optimize (L2O) framework for solving fixed-point problems involving general nonexpansive mappings. Our idea is to deliberately inject summable perturbations into a standard Krasnosel'skii-Mann iteration to improve its average-case performance over a specific distribution of problems while retaining its convergence guarantees. Under a metric sub-regularity assumption, we prove that the proposed parametrization includes only iterations that locally achieve linear convergence-up to a vanishing bias term-and that it encompasses all iterations that do so at a sufficiently fast rate. We then demonstrate how our framework can be used to augment several widely-used operator splitting methods to accelerate the solution of structured monotone inclusion problems, and validate our approach on a best approximation problem using an L2O-augmented Douglas-Rachford splitting algorithm.

Systems and Control (eess.SY); Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2601.07665 [eess.SY]

(or arXiv:2601.07665v2 [eess.SY] for this version)

https://doi.org/10.48550/arXiv.2601.07665 Focus to learn more arXiv-issued DOI via DataCite

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