Zeroth-Order Methods for Stochastic Nonconvex Nonsmooth Composite Optimization

• URL: http://arxiv.org/abs/2510.04446v1
• Date: Mon, 06 Oct 2025 02:35:42 GMT
• Title: Zeroth-Order Methods for Stochastic Nonconvex Nonsmooth Composite Optimization
• Authors: Ziyi Chen, Peiran Yu, Heng Huang,
• Abstract summary: Previous works on composite optimization problem requires the major part to smoothness or some machine learning examples which excludes such two approximate smoothness points respectively.<n>In this work we propose two new algorithms for such problem.<n>We show that these algorithms are effective using numerical experiments.
• Score: 51.63258496873442
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which excludes some machine learning examples such as regularized ReLU network and sparse support matrix machine. In this work, we focus on stochastic nonconvex composite optimization problem without any smoothness assumptions. In particular, we propose two new notions of approximate stationary points for such optimization problem and obtain finite-time convergence results of two zeroth-order algorithms to these two approximate stationary points respectively. Finally, we demonstrate that these algorithms are effective using numerical experiments.

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