[Paper] Decentralized Nonsmooth Nonconvex Optimization with Client Sampling

Source: arXiv - 2601.19381v1

Overview

This paper considers a decentralized nonsmooth nonconvex optimization problem with Lipschitz‑continuous local functions. We propose an efficient stochastic first‑order method with client sampling, achieving the ((\delta,\varepsilon))-Goldstein stationary point with:

• Overall sample complexity: (\mathcal O(\delta^{-1}\varepsilon^{-3}))
• Computation rounds: (\mathcal O(\delta^{-1}\varepsilon^{-3}))
• Communication rounds: (\tilde{\mathcal O}(\gamma^{-1/2}\delta^{-1}\varepsilon^{-3})),

where (\gamma) is the spectral gap of the mixing matrix for the network. Our results attain optimal sample complexity and sharper communication complexity than existing methods. We also extend the ideas to zeroth‑order optimization, and numerical experiments demonstrate the empirical advantage of our methods.

Key Contributions

• math.OC
• cs.DC

Methodology

Please refer to the full paper for detailed methodology.

Practical Implications

This research contributes to the advancement of math.OC.

Authors

• Xinyan Chen
• Weiguo Gao
• Luo Luo

Paper Information

• arXiv ID: 2601.19381v1
• Categories: math.OC, cs.DC
• Published: January 27, 2026
• PDF: Download PDF