A regret minimization approach to fixed-point iterations

Abstract:We propose a conversion scheme that turns regret minimizing algorithms into fixed point iterations, with convergence guarantees following from regret bounds. The resulting iterations can be seen as a grand extension of the classical Krasnoselskii--Mann iterations, as the latter are recovered by converting the Online Gradient Descent algorithm. This approach yields new simple iterations for finding fixed points of non-self operators. We also focus on converting algorithms from the AdaGrad family of regret minimizers, and thus obtain fixed point iterations with adaptive guarantees of a new kind. Numerical experiments on various problems demonstrate faster convergence of AdaGrad-based fixed point iterations over Krasnoselskii--Mann iterations.

Optimization and Control (math.OC); Machine Learning (cs.LG); Numerical Analysis (math.NA)

arXiv:2509.21653 [math.OC]

(or arXiv:2509.21653v2 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2509.21653 Focus to learn more arXiv-issued DOI via DataCite

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