Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees
The authors introduce a Learning to Optimize (L2O) framework to improve standard Krasnosel'skii-Mann iterations by adding small, summable perturbations. This method aims to boost average performance for specific problem distributions while keeping convergence guarantees intact. The framework is shown to work with operator splitting methods and is validated through experiments on a best approximation problem using a Douglas-Rachford algorithm.