Extracting Dual Solutions via Primal Optimizers

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



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Author Details

Yair Carmon
  • Tel Aviv University, Israel
Arun Jambulapati
  • University of Michigan, Ann Arbor, MI, USA
Liam O'Carroll
  • Stanford University, CA, USA
Aaron Sidford
  • Stanford University, CA, USA

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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) https://doi.org/10.4230/LIPIcs.ITCS.2025.29

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Mathematical optimization
Keywords
  • Minimax optimization
  • black-box optimization
  • matrix games
  • distributionally robust optimization

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