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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2603.17053 |
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| _version_ | 1866913160944943104 |
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| author | Krivchenko, Valery Gasnikov, Alexander Kovalev, Dmitry |
| author_facet | Krivchenko, Valery Gasnikov, Alexander Kovalev, Dmitry |
| contents | In this paper, we address the problem of interpolation of smooth convex-concave functions. Interpolation is a key step for computer-assisted estimation of worst-case performance via PEP-like techniques, and smooth convex-concave functions are frequently used to model min-max problems arising in machine learning. We address the challenges associated with deriving conditions that are necessary and sufficient for the interpolation of smooth min-max games and show how existing approaches can be adapted to this setting.
As part of this effort, we study the smoothing properties of Moreau-Yosida-like approximations of convex-concave functions. Next, we derive interpolation conditions for several key special cases of smooth min-max games. Finally, we obtain improved (i.e., tighter) characterizations for smooth strongly monotone convex-concave functions.
We analyze the linear convergence of Alt-GDA using a PEP-like technique with novel constraints and (numerically) obtain a new estimate of its complexity. We are confident that the results of this paper provide meaningful progress toward establishing optimal worst-case guarantees for algorithms in the setting of smooth min-max games. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17053 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strengthening the finite characterizations of smooth min-max games Krivchenko, Valery Gasnikov, Alexander Kovalev, Dmitry Optimization and Control In this paper, we address the problem of interpolation of smooth convex-concave functions. Interpolation is a key step for computer-assisted estimation of worst-case performance via PEP-like techniques, and smooth convex-concave functions are frequently used to model min-max problems arising in machine learning. We address the challenges associated with deriving conditions that are necessary and sufficient for the interpolation of smooth min-max games and show how existing approaches can be adapted to this setting. As part of this effort, we study the smoothing properties of Moreau-Yosida-like approximations of convex-concave functions. Next, we derive interpolation conditions for several key special cases of smooth min-max games. Finally, we obtain improved (i.e., tighter) characterizations for smooth strongly monotone convex-concave functions. We analyze the linear convergence of Alt-GDA using a PEP-like technique with novel constraints and (numerically) obtain a new estimate of its complexity. We are confident that the results of this paper provide meaningful progress toward establishing optimal worst-case guarantees for algorithms in the setting of smooth min-max games. |
| title | Strengthening the finite characterizations of smooth min-max games |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.17053 |