Year: 2026
Type: preprint
Abstract: We consider the problem of finding stationary points of stochastic convex functions and related variational inequalities. For each, we show that regularized empirical risk minimization, coupled with a random tilting perturbation, obtains stationarity residual order $\sqrt{d/n}$ for $d$-dimensional problems given $n$ observations. We present a few complementary results that show that some dimension dependence is necessary, in distinction from standard stochastic optimization and empirical risk minimization, by providing minimax lower bounds scaling as $\sqrt{\log d / n}$.
Source: arXiv (Cornell University)
Authors: Areces, Felipe, Duchi, John C., Sommers, Malo
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213515285