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arXiv Machine Learning By Andrea Martin, Giuseppe Belgioioso

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

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The paper presents a learning-to-optimize (L2O) framework that injects summable perturbations into Krasnosel'skii-Mann iterations to accelerate solving fixed-point problems with nonexpansive mappings. It proves that, under metric sub-regularity, the parametrized iterations achieve local linear convergence with a vanishing bias and include all fast-converging iterations. The framework is applied to enhance operator splitting methods, such as Douglas‑Rachford, and is validated on a best‑approximation problem.

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