{"ID":2866246,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.21653","arxiv_id":"2509.21653","title":"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.","short_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 Gr...","url_abs":"https://arxiv.org/abs/2509.21653","url_pdf":"https://arxiv.org/pdf/2509.21653v1","authors":"[\"Joon Kwon\"]","published":"2025-09-25T22:13:30Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\",\"math.NA\"]","methods":"[]","has_code":false}