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DOI: 10.4230/LIPIcs.ITCS.2025.29

Extracting Dual Solutions via Primal Optimizers

Authors: Yair Carmon, Arun Jambulapati, Liam O'Carroll, and Aaron Sidford

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

We provide a general method to convert a "primal" black-box algorithm for solving regularized convex-concave minimax optimization problems into an algorithm for solving the associated dual maximin optimization problem. Our method adds recursive regularization over a logarithmic number of rounds where each round consists of an approximate regularized primal optimization followed by the computation of a dual best response. We apply this result to obtain new state-of-the-art runtimes for solving matrix games in specific parameter regimes, obtain improved query complexity for solving the dual of the CVaR distributionally robust optimization (DRO) problem, and recover the optimal query complexity for finding a stationary point of a convex function.

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Yair Carmon, Arun Jambulapati, Liam O'Carroll, and Aaron Sidford. Extracting Dual Solutions via Primal Optimizers. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 29:1-29:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{carmon_et_al:LIPIcs.ITCS.2025.29,
  author =	{Carmon, Yair and Jambulapati, Arun and O'Carroll, Liam and Sidford, Aaron},
  title =	{{Extracting Dual Solutions via Primal Optimizers}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{29:1--29:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.29},
  URN =		{urn:nbn:de:0030-drops-226578},
  doi =		{10.4230/LIPIcs.ITCS.2025.29},
  annote =	{Keywords: Minimax optimization, black-box optimization, matrix games, distributionally robust optimization}
}

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Extracting Dual Solutions via Primal Optimizers

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