Stochastic variance reduced extragradient methods for solving hierarchical variational inequalities
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917274556825600 |
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| author | Dvurechensky, Pavel Ebner, Andrea Schnebel, Johannes Carl Shtern, Shimrit Staudigl, Mathias |
| author_facet | Dvurechensky, Pavel Ebner, Andrea Schnebel, Johannes Carl Shtern, Shimrit Staudigl, Mathias |
| contents | We are concerned with optimization in a broad sense through the lens of solving variational inequalities (VIs) -- a class of problems that are so general that they cover as particular cases minimization of functions, saddle-point (minimax) problems, Nash equilibrium problems, and many others. The key challenges in our problem formulation are the two-level hierarchical structure and finite-sum representation of the smooth operators in each level. For this setting, we are the first to prove convergence rates and complexity statements for variance-reduced stochastic algorithms approaching the solution of hierarchical VIs in Euclidean and Bregman setups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13510 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic variance reduced extragradient methods for solving hierarchical variational inequalities Dvurechensky, Pavel Ebner, Andrea Schnebel, Johannes Carl Shtern, Shimrit Staudigl, Mathias Optimization and Control Computer Science and Game Theory Machine Learning We are concerned with optimization in a broad sense through the lens of solving variational inequalities (VIs) -- a class of problems that are so general that they cover as particular cases minimization of functions, saddle-point (minimax) problems, Nash equilibrium problems, and many others. The key challenges in our problem formulation are the two-level hierarchical structure and finite-sum representation of the smooth operators in each level. For this setting, we are the first to prove convergence rates and complexity statements for variance-reduced stochastic algorithms approaching the solution of hierarchical VIs in Euclidean and Bregman setups. |
| title | Stochastic variance reduced extragradient methods for solving hierarchical variational inequalities |
| topic | Optimization and Control Computer Science and Game Theory Machine Learning |
| url | https://arxiv.org/abs/2602.13510 |