arXiv：cs.LG· Andrea Martin, Giuseppe Belgioioso·· 13 小时前
用可保证收敛的学习优化加速 Krasnosel'skii-Mann 不动点迭代
Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees
AI 导读
研究者提出一种有原则的学习优化（L2O）框架，通过向标准 Krasnosel'skiĭ-Mann 迭代注入可和扰动，在保持收敛保证的同时提升其在特定问题分布上的平均性能。
正文
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.
| Subjects: | Systems and Control (eess.SY); Machine Learning (cs.LG); Optimization and Control (math.OC) |
| Cite as: | arXiv:2601.07665 [eess.SY] |
| (or arXiv:2601.07665v2 [eess.SY] for this version) | |
| https://doi.org/10.48550/arXiv.2601.07665 arXiv-issued DOI via DataCite |
Submission history
From: Andrea Martin [view email]
[v1]
Mon, 12 Jan 2026 15:45:40 UTC (859 KB)
[v2]
Fri, 9 Oct 2026 13:01:17 UTC (859 KB)
来源：arXiv：cs.LG · arxiv.org