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The Role of Gradient Modification in Heavy-Tailed Nonconvex Stochastic Min-Max Optimization

arXiv · AI, language, vision and robotics · article · Sep 5, 2026 · UTC

Stochastic min-max optimization has attracted increasing attention due to its applications in modern machine learning, while existing theoretical studies mainly rely on the bounded variance assumption for stochastic gradients. Under heavy-tailed noise, where stochastic gradients only possess a finite $p$-th moment for $p\in(1,2]$, gradient clipping or normalization is commonly believed to be necessary to guarantee convergence. In this work, we revisit stochastic min-max optimization under heavy-tailed noise and provide a comprehensive theoretical study of stochastic gradient descent ascent (SG

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