Accelerated variance-reduced methods for saddle-point problems

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 acceler...

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Veröffentlicht in:EURO journal on computational optimization Jg. 10; S. 100048
Hauptverfasser: Borodich, Ekaterina, Tominin, Vladislav, Tominin, Yaroslav, Kovalev, Dmitry, Gasnikov, Alexander, Dvurechensky, Pavel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 2022
Elsevier
Schlagworte:
Accelerated algorithms
Composite optimization
Minimax optimization
Saddle-point problem
Stochastic variance-reduced algorithms
Minimax optimization
Composite optimization
Saddle-point problem
Accelerated algorithms
Stochastic variance-reduced algorithms
ISSN:2192-4406
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Zusammenfassung: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. •Optimal accelerated stochastic variance-reduced algorithm for composite saddle-point problems.•Saddle-point problems with different strongly-convex and strongly-concave parameters.•Upper bounds for composite saddle-point problems with a finite sum structure.•Achieving the lower bounds for composite saddle-point problems with finite sum structure up to logarithmic factor.
ISSN:2192-4406
DOI:10.1016/j.ejco.2022.100048