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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.12334 |
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| _version_ | 1866909817065439232 |
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| author | Vankov, Daniil Nedich, Angelia Sankar, Lalitha |
| author_facet | Vankov, Daniil Nedich, Angelia Sankar, Lalitha |
| contents | This paper focuses on solving a stochastic variational inequality (SVI) problem under relaxed smoothness assumption for a class of structured non-monotone operators. The SVI problem has attracted significant interest in the machine learning community due to its immediate application to adversarial training and multi-agent reinforcement learning. In many such applications, the resulting operators do not satisfy the smoothness assumption. To address this issue, we focus on a weaker generalized smoothness assumption called $α$-symmetric. Under $p$-quasi sharpness and $α$-symmetric assumptions on the operator, we study clipped projection (gradient descent-ascent) and clipped Korpelevich (extragradient) methods. For these clipped methods, we provide the first almost-sure convergence results without making any assumptions on the boundedness of either the stochastic operator or the stochastic samples. We also provide the first in-expectation unbiased convergence rate results for these methods under a relaxed smoothness assumption for $α\leq \frac{1}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12334 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Smooth Stochastic Variational Inequalities: Almost Sure Convergence and Convergence Rates Vankov, Daniil Nedich, Angelia Sankar, Lalitha Optimization and Control This paper focuses on solving a stochastic variational inequality (SVI) problem under relaxed smoothness assumption for a class of structured non-monotone operators. The SVI problem has attracted significant interest in the machine learning community due to its immediate application to adversarial training and multi-agent reinforcement learning. In many such applications, the resulting operators do not satisfy the smoothness assumption. To address this issue, we focus on a weaker generalized smoothness assumption called $α$-symmetric. Under $p$-quasi sharpness and $α$-symmetric assumptions on the operator, we study clipped projection (gradient descent-ascent) and clipped Korpelevich (extragradient) methods. For these clipped methods, we provide the first almost-sure convergence results without making any assumptions on the boundedness of either the stochastic operator or the stochastic samples. We also provide the first in-expectation unbiased convergence rate results for these methods under a relaxed smoothness assumption for $α\leq \frac{1}{2}$. |
| title | Generalized Smooth Stochastic Variational Inequalities: Almost Sure Convergence and Convergence Rates |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2410.12334 |