Zeroth-Order Algorithms for Smooth Saddle-Point Problems
It addresses saddle-point problems in machine learning, such as GAN training, where only zeroth-order information is available, offering an incremental improvement over existing methods.
The paper tackles stochastic smooth convex-concave saddle-point problems using zeroth-order oracles, achieving a convergence rate only a log n factor worse than first-order methods for specific feasible sets, and demonstrates practical performance on real-world problems.
Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using stochastic gradients. At the same time, in some applications only a zeroth-order oracle is available. In this paper, we propose several algorithms to solve stochastic smooth (strongly) convex-concave saddle-point problems using zeroth-order oracles and estimate their convergence rate and its dependence on the dimension $n$ of the variable. In particular, our analysis shows that in the case when the feasible set is a direct product of two simplices, our convergence rate for the stochastic term is only by a $\log n$ factor worse than for the first-order methods. We also consider a mixed setup and develop 1/2th-order methods that use zeroth-order oracle for the minimization part and first-order oracle for the maximization part. Finally, we demonstrate the practical performance of our zeroth-order and 1/2th-order methods on practical problems.