A Parameter-free Decentralized Algorithm for Composite Convex Optimization
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908476846899200 |
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| author | Chen, Xiaokai Kuruzov, Ilya Scutari, Gesualdo Gasnikov, Alexander |
| author_facet | Chen, Xiaokai Kuruzov, Ilya Scutari, Gesualdo Gasnikov, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01466 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Parameter-free Decentralized Algorithm for Composite Convex Optimization Chen, Xiaokai Kuruzov, Ilya Scutari, Gesualdo Gasnikov, Alexander Optimization and Control 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. |
| title | A Parameter-free Decentralized Algorithm for Composite Convex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.01466 |