Variance-reduction for Variational Inequality Problems with Bregman Distance Function
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911064949522432 |
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| author | Alizadeh, Zeinab Hamedani, Erfan Yazdandoost Jalilzadeh, Afrooz |
| author_facet | Alizadeh, Zeinab Hamedani, Erfan Yazdandoost Jalilzadeh, Afrooz |
| contents | In this paper, we address variational inequalities (VI) with a finite-sum structure. We introduce a novel single-loop stochastic variance-reduced algorithm, incorporating the Bregman distance function, and establish an optimal convergence guarantee under a monotone setting. Additionally, we explore a structured class of non-monotone problems that exhibit weak Minty solutions, and analyze the complexity of our proposed method, highlighting a significant improvement over existing approaches. Numerical experiments are presented to demonstrate the performance of our algorithm compared to state-of-the-art methods |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variance-reduction for Variational Inequality Problems with Bregman Distance Function Alizadeh, Zeinab Hamedani, Erfan Yazdandoost Jalilzadeh, Afrooz Optimization and Control In this paper, we address variational inequalities (VI) with a finite-sum structure. We introduce a novel single-loop stochastic variance-reduced algorithm, incorporating the Bregman distance function, and establish an optimal convergence guarantee under a monotone setting. Additionally, we explore a structured class of non-monotone problems that exhibit weak Minty solutions, and analyze the complexity of our proposed method, highlighting a significant improvement over existing approaches. Numerical experiments are presented to demonstrate the performance of our algorithm compared to state-of-the-art methods |
| title | Variance-reduction for Variational Inequality Problems with Bregman Distance Function |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2405.10735 |