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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.05669 |
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| _version_ | 1866908503140990976 |
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| author | Vyguzov, A. A. Stonyakin, F. S. |
| author_facet | Vyguzov, A. A. Stonyakin, F. S. |
| contents | We study the Frank-Wolfe algorithm for constrained optimization problems with relatively smooth objectives. Building upon our previous work, we propose a fully adaptive variant of the Frank-Wolfe method that dynamically adjusts the step size. Our method does not require prior knowledge of the function parameters and guarantees convergence using only local information. We establish a linear convergence rate under relative strong convexity and provide a detailed theoretical analysis of the proposed adaptive step-size rule.
Furthermore, we demonstrate how relative smoothness and strong convexity naturally arise in the setting of centralized distributed optimization. Under a variance-type assumption on the gradients, we show that the global objective becomes relatively strongly convex with respect to the Bregman divergence generated by a local function. This structure allows us to apply our adaptive Frank-Wolfe algorithm, leading to provable acceleration due to an improved relative condition number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Fully Adaptive Frank-Wolfe Algorithm for Relatively Smooth Problems and Its Application to Centralized Distributed Optimization Vyguzov, A. A. Stonyakin, F. S. Optimization and Control We study the Frank-Wolfe algorithm for constrained optimization problems with relatively smooth objectives. Building upon our previous work, we propose a fully adaptive variant of the Frank-Wolfe method that dynamically adjusts the step size. Our method does not require prior knowledge of the function parameters and guarantees convergence using only local information. We establish a linear convergence rate under relative strong convexity and provide a detailed theoretical analysis of the proposed adaptive step-size rule. Furthermore, we demonstrate how relative smoothness and strong convexity naturally arise in the setting of centralized distributed optimization. Under a variance-type assumption on the gradients, we show that the global objective becomes relatively strongly convex with respect to the Bregman divergence generated by a local function. This structure allows us to apply our adaptive Frank-Wolfe algorithm, leading to provable acceleration due to an improved relative condition number. |
| title | A Fully Adaptive Frank-Wolfe Algorithm for Relatively Smooth Problems and Its Application to Centralized Distributed Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.05669 |