{"ID":2887684,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.01466","arxiv_id":"2508.01466","title":"A Parameter-free Decentralized Algorithm for Composite Convex Optimization","abstract":"The paper studies decentralized optimization over networks, where agents minimize a composite objective consisting of the sum of smooth convex functions--the agents' losses--and an additional nonsmooth convex extended value function. We propose a decentralized algorithm wherein agents ${\\it adaptively}$ adjust their stepsize using local backtracking procedures that require ${\\it no}$ ${\\it global}$ (network) information or extensive inter-agent communications. Our adaptive decentralized method enjoys robust convergence guarantees, outperforming existing decentralized methods, which are not adaptive. Our design is centered on a three-operator splitting, applied to a reformulation of the optimization problem. This reformulation utilizes a proposed BCV metric, which facilitates decentralized implementation and local stepsize adjustments while guarantying convergence.","short_abstract":"The paper studies decentralized optimization over networks, where agents minimize a composite objective consisting of the sum of smooth convex functions--the agents' losses--and an additional nonsmooth convex extended value function. We propose a decentralized algorithm wherein agents ${\\it adaptively}$ adjust their st...","url_abs":"https://arxiv.org/abs/2508.01466","url_pdf":"https://arxiv.org/pdf/2508.01466v1","authors":"[\"Xiaokai Chen\",\"Ilya Kuruzov\",\"Gesualdo Scutari\",\"Alexander Gasnikov\"]","published":"2025-08-02T18:53:34Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}