Min-Max Optimization Requires Exponentially Many Queries

• URL: http://arxiv.org/abs/2605.13806v1
• Date: Wed, 13 May 2026 17:34:24 GMT
• Title: Min-Max Optimization Requires Exponentially Many Queries
• Abstract summary: query complexity of a non min-nonconcave function $f$ $[0,1].<n>We show that queries to $f$ and its gradient point must make a point that is exponential in $1 ord$.
• Score: 71.85811744604827
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $d$.

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