On the application of Danskin's theorem to derivative-free minimax problems
Abstract
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 descent directions. 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.
- Publication:
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Proceedings LEGO - 14th International Global Optimization Workshop
- Pub Date:
- February 2019
- DOI:
- 10.1063/1.5089993
- arXiv:
- arXiv:1805.06322
- Bibcode:
- 2019AIPC.2070b0026A
- Keywords:
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- Mathematics - Optimization and Control;
- Computer Science - Numerical Analysis
- E-Print:
- Submitted to LEGO 2018 (14th Int. Workshop on Global Optimization)