Min-Max Optimization Requires Exponentially Many Queries

Fuente: arXiv
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Main Authors: Bernasconi, Martino, Castiglioni, Matteo, Celli, Andrea, Hollender, Alexandros
Format: Preprint
Published: 2026
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author Bernasconi, Martino
Castiglioni, Matteo
Celli, Andrea
Hollender, Alexandros
author_facet Bernasconi, Martino
Castiglioni, Matteo
Celli, Andrea
Hollender, Alexandros
contents We study the query complexity of min-max optimization of a nonconvex-nonconcave function $f$ over $[0,1]^d \times [0,1]^d$. We show that, given oracle access to $f$ and to its gradient $\nabla f$, any algorithm that finds an $\varepsilon$-approximate stationary point must make a number of queries that is exponential in $1/\varepsilon$ or $d$.
format Preprint
id arxiv_https___arxiv_org_abs_2605_13806
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Min-Max Optimization Requires Exponentially Many Queries
Bernasconi, Martino
Castiglioni, Matteo
Celli, Andrea
Hollender, Alexandros
Data Structures and Algorithms
Computational Complexity
Computer Science and Game Theory
Machine Learning
Optimization and Control
We study the query complexity of min-max optimization of a nonconvex-nonconcave function $f$ over $[0,1]^d \times [0,1]^d$. We show that, given oracle access to $f$ and to its gradient $\nabla f$, any algorithm that finds an $\varepsilon$-approximate stationary point must make a number of queries that is exponential in $1/\varepsilon$ or $d$.
title Min-Max Optimization Requires Exponentially Many Queries
topic Data Structures and Algorithms
Computational Complexity
Computer Science and Game Theory
Machine Learning
Optimization and Control
url https://arxiv.org/abs/2605.13806