Gradient-Free Algorithms for Solving Stochastic Saddle Optimization Problems With the Polyak–loyasievich Condition
S. I. Sadykov,
A. V. Lobanov,
A. M. Raigorodskii
Abstract:This paper focuses on solving a subclass of a stochastic nonconvex-concave black box optimization problem with a saddle point that satisfies the Polyak–Loyasievich condition. To solve such a problem, we provide the first, to our knowledge, gradient-free algorithm, the approach to which is based on applying a gradient approximation (kernel approximation) to the oracle-shifted stochastic gradient descent algorithm. We present theoretical estimates that guarantee a global linear rate of convergence to the desired… Show more
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