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Decentralized saddle-point problems with different constants of strong convexity and strong concavity

Author

Listed:
  • Dmitry Metelev

    (Moscow Institute of Physics and Technology)

  • Alexander Rogozin

    (Moscow Institute of Physics and Technology
    HSE University)

  • Alexander Gasnikov

    (Moscow Institute of Physics and Technology
    HSE University
    ISP RAS Research Center for Trusted Artificial Intelligence)

  • Dmitry Kovalev

    (King Abdullah University of Science and Technology)

Abstract

Large-scale saddle-point problems arise in such machine learning tasks as GANs and linear models with affine constraints. In this paper, we study distributed saddle-point problems with strongly-convex–strongly-concave smooth objectives that have different strong convexity and strong concavity parameters of composite terms, which correspond to min and max variables, and bilinear saddle-point part. We consider two types of first-order oracles: deterministic (returns gradient) and stochastic (returns unbiased stochastic gradient). Our method works in both cases and takes several consensus steps between oracle calls.

Suggested Citation

  • Dmitry Metelev & Alexander Rogozin & Alexander Gasnikov & Dmitry Kovalev, 2024. "Decentralized saddle-point problems with different constants of strong convexity and strong concavity," Computational Management Science, Springer, vol. 21(1), pages 1-41, June.
    • Handle: RePEc:spr:comgts:v:21:y:2024:i:1:d:10.1007_s10287-023-00485-9
    DOI: 10.1007/s10287-023-00485-9
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