Min-Max Optimization Requires Exponentially Many Queries
Data Structures and Algorithms
2026-05-14 v1 Computational Complexity
Computer Science and Game Theory
Machine Learning
Optimization and Control
Abstract
We study the query complexity of min-max optimization of a nonconvex-nonconcave function over . We show that, given oracle access to and to its gradient , any algorithm that finds an -approximate stationary point must make a number of queries that is exponential in or .
Cite
@article{arxiv.2605.13806,
title = {Min-Max Optimization Requires Exponentially Many Queries},
author = {Martino Bernasconi and Matteo Castiglioni and Andrea Celli and Alexandros Hollender},
journal= {arXiv preprint arXiv:2605.13806},
year = {2026}
}