# On the Application of Danskin's Theorem to Derivative-Free Minimax Optimization

arXiv: https://arxiv.org/abs/1805.06322 · HTML: https://mlsanity.com/paper/1805.06322/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2018.

## Built on by (most cited first, 1 of 1)

- [Derivative-free Alternating Projection Algorithms for General Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/2108.00473/) (2021)

## Abstract (arXiv)

Motivated by Danskin's theorem, gradient-based methods have been applied with empirical success to solve minimax problems that involve non-convex outer minimization and non-concave inner maximization. On the other hand, recent work has demonstrated that Evolution Strategies (ES) algorithms are stochastic gradient approximators that seek robust solutions. In this paper, we address black-box (gradient-free) minimax problems that have long been tackled in a coevolutionary setup. To this end and guaranteed by Danskin's theorem, we employ ES as a stochastic estimator for the descent direction. The proposed approach is validated on a collection of black-box minimax problems. Based on our experiments, our method's performance is comparable with its coevolutionary counterparts and favorable for high-dimensional problems. Its efficacy is demonstrated on a real-world application.