Min-Max Optimization Requires Exponentially Many Queries

Martino Bernasconi; Matteo Castiglioni; Andrea Celli; Alexandros Hollender

Min-Max Optimization Requires Exponentially Many Queries

数据结构与算法 2026-05-14 v1 计算复杂性计算机科学与博弈论机器学习最优化与控制

作者: Martino Bernasconi , Matteo Castiglioni , Andrea Celli , Alexandros Hollender

摘要

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 $d$ .

关键词

convex optimization approximation algorithm

引用

@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}
}

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