Adaptive Decentralized Composite Optimization via Three-Operator Splitting
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917282765078528 |
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| author | Chen, Xiaokai Kuruzov, Ilya Scutari, Gesualdo |
| author_facet | Chen, Xiaokai Kuruzov, Ilya Scutari, Gesualdo |
| contents | The paper studies decentralized optimization over networks, where agents minimize a sum of {\it locally} smooth (strongly) convex losses and plus a nonsmooth convex extended value term. We propose decentralized methods wherein agents {\it adaptively} adjust their stepsize via local backtracking procedures coupled with lightweight min-consensus protocols. Our design stems from a three-operator splitting factorization applied to an equivalent reformulation of the problem. The reformulation is endowed with a new BCV preconditioning metric (Bertsekas-O'Connor-Vandenberghe), which enables efficient decentralized implementation and local stepsize adjustments. We establish robust convergence guarantees. Under mere convexity, the proposed methods converge with a sublinear rate. Under strong convexity of the sum-function, and assuming the nonsmooth component is partly smooth, we further prove linear convergence. Numerical experiments corroborate the theory and highlight the effectiveness of the proposed adaptive stepsize strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17545 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive Decentralized Composite Optimization via Three-Operator Splitting Chen, Xiaokai Kuruzov, Ilya Scutari, Gesualdo Optimization and Control Machine Learning Multiagent Systems The paper studies decentralized optimization over networks, where agents minimize a sum of {\it locally} smooth (strongly) convex losses and plus a nonsmooth convex extended value term. We propose decentralized methods wherein agents {\it adaptively} adjust their stepsize via local backtracking procedures coupled with lightweight min-consensus protocols. Our design stems from a three-operator splitting factorization applied to an equivalent reformulation of the problem. The reformulation is endowed with a new BCV preconditioning metric (Bertsekas-O'Connor-Vandenberghe), which enables efficient decentralized implementation and local stepsize adjustments. We establish robust convergence guarantees. Under mere convexity, the proposed methods converge with a sublinear rate. Under strong convexity of the sum-function, and assuming the nonsmooth component is partly smooth, we further prove linear convergence. Numerical experiments corroborate the theory and highlight the effectiveness of the proposed adaptive stepsize strategy. |
| title | Adaptive Decentralized Composite Optimization via Three-Operator Splitting |
| topic | Optimization and Control Machine Learning Multiagent Systems |
| url | https://arxiv.org/abs/2602.17545 |