English

Integral control of the proximal gradient method for unbiased sparse optimization

Optimization and Control 2025-04-18 v1 Systems and Control Systems and Control

Abstract

Proximal gradient methods are popular in sparse optimization as they are straightforward to implement. Nevertheless, they achieve biased solutions, requiring many iterations to converge. This work addresses these issues through a suitable feedback control of the algorithm's hyperparameter. Specifically, by designing an integral control that does not substantially impact the computational complexity, we can reach an unbiased solution in a reasonable number of iterations. In the paper, we develop and analyze the convergence of the proposed approach for strongly-convex problems. Moreover, numerical simulations validate and extend the theoretical results to the non-strongly convex framework.

Keywords

Cite

@article{arxiv.2504.12814,
  title  = {Integral control of the proximal gradient method for unbiased sparse optimization},
  author = {V. Cerone and S. M. Fosson and A. Re and D. Regruto},
  journal= {arXiv preprint arXiv:2504.12814},
  year   = {2025}
}
R2 v1 2026-06-28T23:01:50.107Z