# A Novel Catalyst Scheme for Stochastic Minimax Optimization

arXiv: https://arxiv.org/abs/2311.02814 · HTML: https://mlsanity.com/paper/2311.02814/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2023.

## Built on by (most cited first, 2 of 2)

- [How to Make the Gradient Mapping Small for Constrained Stochastic Min-Max Problems and Beyond](https://mlsanity.com/paper/2609.08380/) (2026)
- [Accelerating Distributed Optimization: A Primal-Dual Perspective on Local Steps](https://mlsanity.com/paper/2407.02689/) (2024)

## Abstract (arXiv)

This paper presents a proximal-point-based catalyst scheme for simple first-order methods applied to convex minimization and convex-concave minimax problems. In particular, for smooth and (strongly)-convex minimization problems, the proposed catalyst scheme, instantiated with a simple variant of stochastic gradient method, attains the optimal rate of convergence in terms of both deterministic and stochastic errors. For smooth and strongly-convex-strongly-concave minimax problems, the catalyst scheme attains the optimal rate of convergence for deterministic and stochastic errors up to a logarithmic factor. To the best of our knowledge, this reported convergence seems to be attained for the first time by stochastic first-order methods in the literature. We obtain this result by designing and catalyzing a novel variant of stochastic extragradient method for solving smooth and strongly-monotone variational inequality, which may be of independent interest.