• Media type: E-Article; Text
  • Title: Accelerated variance-reduced methods for saddle-point problems
  • Contributor: Borodich, Ekaterina [Author]; Tominin, Vladislav [Author]; Tominin, Yaroslav [Author]; Kovalev, Dmitry [Author]; Gasnikov, Alexander [Author]; Dvurechensky, Pavel [Author]
  • imprint: Amsterdam : Elsevier, 2022
  • Published in: EURO journal on computational optimization 10 (2022)
  • Issue: published Version
  • Language: English
  • DOI: https://doi.org/10.34657/10658; https://doi.org/10.1016/j.ejco.2022.100048
  • ISSN: 2192-4406
  • Keywords: Minimax optimization ; Composite optimization ; Stochastic variance-reduced algorithms ; Accelerated algorithms ; Saddle-point problem
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  • Description: We consider composite minimax optimization problems where the goal is to find a saddle-point of a large sum of non-bilinear objective functions augmented by simple composite regularizers for the primal and dual variables. For such problems, under the average-smoothness assumption, we propose accelerated stochastic variance-reduced algorithms with optimal up to logarithmic factors complexity bounds. In particular, we consider strongly-convex-strongly-concave, convex-strongly-concave, and convex-concave objectives. To the best of our knowledge, these are the first nearly-optimal algorithms for this setting.
  • Access State: Open Access