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arXiv · 2305.15828

Highly Smoothness Zero-Order Methods for Solving Optimization Problems under PL Condition

Aleksandr Lobanov·Alexander Gasnikov·Fedor Stonyakin
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Abstract

In this paper, we study the black box optimization problem under the Polyak--Lojasiewicz (PL) condition, assuming that the objective function is not just smooth, but has higher smoothness. By using "kernel-based" approximation instead of the exact gradient in Stochastic Gradient Descent method, we improve the best known results of convergence in the class of gradient-free algorithms solving problem under PL condition. We generalize our results to the case where a zero-order oracle returns a function value at a point with some adversarial noise. We verify our theoretical results on the example of solving a system of nonlinear equations.

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Aleksandr Lobanov, Alexander Gasnikov, Fedor Stonyakin. 2023-05-25. Highly Smoothness Zero-Order Methods for Solving Optimization Problems under PL Condition. https://arxiv.org/abs/2305.15828

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