Zeroth-Order Nonconvex Nonsmooth Optimization with Heavy-Tailed Noise
This paper considers the nonconvex nonsmooth problem in which the objective function is Lipschitz continuous. We focus on the stochastic setting where the algorithm can access stochastic function value evaluations with heavy-tailed noise, which is prevalent in many popular machine learning applications. We propose a stochastic zeroth-order algorithm that refines the framework of online-to-nonconvex conversion by clipping the two-point gradient estimator. The theoretical analysis shows that our algorithm can find a $(δ, ε)$-Goldstein stationary point with zeroth-order oracle complexity of ${\mathcal O}(d^{\frac{p}{2(p-1)}}δ^{-1}ε^{-\frac{2p-1}{p-1}})$, where $d$ is the problem dimension an...
| Authors | Zhuanghua Liu, Luo Luo |
|---|---|
| Primary category | cs.LG |
| Published | 23 May 2026 |
| Last updated at source | 23 May 2026 |
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