Adaptive Stepsize Selection in Decentralized Convex Optimization
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| author | Kuruzov, Ilya Chen, Xiaokai Scutari, Gesualdo Gasnikov, Alexander |
| author_facet | Kuruzov, Ilya Chen, Xiaokai Scutari, Gesualdo Gasnikov, Alexander |
| contents | We study decentralized optimization where multiple agents minimize the average of their (strongly) convex, smooth losses over a communication graph. Convergence of the existing decentralized methods generally hinges on an apriori, proper selection of the stepsize. Choosing this value is notoriously delicate: (i) it demands global knowledge from all the agents of the graph's connectivity and every local smoothness/strong-convexity constants--information they rarely have; (ii) even with perfect information, the worst-case tuning forces an overly small stepsize, slowing convergence in practice; and (iii) large-scale trial-and-error tuning is prohibitive. This work introduces a decentralized algorithm that is fully adaptive in the choice of the agents' stepsizes, without any global information and using only neighbor-to-neighbor communications--agents need not even know whether the problem is strongly convex. The algorithm retains strong guarantees: it converges at \emph{linear} rate when the losses are strongly convex and at \emph{sublinear} rate otherwise, matching the best-known rates of (nonadaptive) parameter-dependent methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23725 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Stepsize Selection in Decentralized Convex Optimization Kuruzov, Ilya Chen, Xiaokai Scutari, Gesualdo Gasnikov, Alexander Optimization and Control We study decentralized optimization where multiple agents minimize the average of their (strongly) convex, smooth losses over a communication graph. Convergence of the existing decentralized methods generally hinges on an apriori, proper selection of the stepsize. Choosing this value is notoriously delicate: (i) it demands global knowledge from all the agents of the graph's connectivity and every local smoothness/strong-convexity constants--information they rarely have; (ii) even with perfect information, the worst-case tuning forces an overly small stepsize, slowing convergence in practice; and (iii) large-scale trial-and-error tuning is prohibitive. This work introduces a decentralized algorithm that is fully adaptive in the choice of the agents' stepsizes, without any global information and using only neighbor-to-neighbor communications--agents need not even know whether the problem is strongly convex. The algorithm retains strong guarantees: it converges at \emph{linear} rate when the losses are strongly convex and at \emph{sublinear} rate otherwise, matching the best-known rates of (nonadaptive) parameter-dependent methods. |
| title | Adaptive Stepsize Selection in Decentralized Convex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.23725 |