# Decentralized Gradient-Free Methods for Stochastic Non-Smooth Non-Convex Optimization

arXiv: https://arxiv.org/abs/2310.11973 · HTML: https://mlsanity.com/paper/2310.11973/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2023.

## Built on by (most cited first, 5 of 5)

- [Online Optimization Perspective on First-Order and Zero-Order Decentralized Nonsmooth Nonconvex Stochastic Optimization](https://mlsanity.com/paper/2406.01484/) (2024)
- [Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds](https://mlsanity.com/paper/2509.07779/) (2025)
- [Double Variance Reduction: A Smoothing Trick for Composite Optimization Problems without First-Order Gradient](https://mlsanity.com/paper/2405.17761/) (2024)
- [The Exponential Price of Determinism in Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2609.23837/) (2026)
- [Dimension-Free Decentralized Nonsmooth Nonconvex Stochastic Optimization](https://mlsanity.com/paper/2610.05789/) (2026)

## Abstract (arXiv)

We consider decentralized gradient-free optimization of minimizing Lipschitz continuous functions that satisfy neither smoothness nor convexity assumption. We propose two novel gradient-free algorithms, the Decentralized Gradient-Free Method (DGFM) and its variant, the Decentralized Gradient-Free Method^+ (DGFM+). Based on the techniques of randomized smoothing and gradient tracking, DGFM requires the computation of the zeroth-order oracle of a single sample in each iteration, making it less demanding in terms of computational resources for individual computing nodes. Theoretically, DGFM achieves a complexity of mathcal O(d3/2δ-1varepsilon -4) for obtaining an (δ,varepsilon)-Goldstein stationary point. DGFM+, an advanced version of DGFM, incorporates variance reduction to further improve the convergence behavior. It samples a mini-batch at each iteration and periodically draws a larger batch of data, which improves the complexity to mathcal O(d3/2δ-1 varepsilon-3). Moreover, experimental results underscore the empirical advantages of our proposed algorithms when applied to real-world datasets.