dorsal/arxiv
View SchemaLearning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees
| Authors | Andrea Martin, Giuseppe Belgioioso |
|---|---|
| Categories | |
| ArXiv ID | 2601.07665vv1 |
| URL | https://arxiv.org/abs/2601.07665 |
| License | http://creativecommons.org/licenses/by/4.0/ |
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.
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"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\u0027skii-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.",
"arxiv_id": "2601.07665",
"authors": [
"Andrea Martin",
"Giuseppe Belgioioso"
],
"categories": [
"eess.SY",
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],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Learning to accelerate Krasnosel\u0027skii-Mann fixed-point iterations with guarantees",
"url": "https://arxiv.org/abs/2601.07665",
"version": "v1"
},
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