# Generalized Smooth Stochastic Variational Inequalities: Almost Sure Convergence and Convergence Rates

arXiv: https://arxiv.org/abs/2410.12334 · HTML: https://mlsanity.com/paper/2410.12334/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2024.

## Built on by (most cited first, 1 of 1)

- [Adaptive Gradient Normalization and Independent Sampling for (Stochastic) Generalized-Smooth Optimization](https://mlsanity.com/paper/2410.14054/) (2024)

## Abstract (arXiv)

This paper focuses on solving a stochastic variational inequality (SVI) problem under relaxed smoothness assumption for a class of structured non-monotone operators. The SVI problem has attracted significant interest in the machine learning community due to its immediate application to adversarial training and multi-agent reinforcement learning. In many such applications, the resulting operators do not satisfy the smoothness assumption. To address this issue, we focus on a weaker generalized smoothness assumption called α-symmetric. Under p-quasi sharpness and α-symmetric assumptions on the operator, we study clipped projection (gradient descent-ascent) and clipped Korpelevich (extragradient) methods. For these clipped methods, we provide the first almost-sure convergence results without making any assumptions on the boundedness of either the stochastic operator or the stochastic samples. We also provide the first in-expectation unbiased convergence rate results for these methods under a relaxed smoothness assumption for α ≤ frac12.