We show how evolution strategies, which are stochastic gradient approximators, can be used to solve min-max problems.
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Motivated by Danskin’s, 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, 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.