2024/03/18 by Siyuan Zhang, Zhang, Siyuan, Nachuan Xiao +3
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2403.11565
openalex publication_date 2024/03/18 · openalex created_date 2024/03/20 · openalex updated_date 2026/07/28
In this paper, we focus on the decentralized stochastic subgradient-based methods in minimizing nonsmooth nonconvex functions without Clarke regularity, especially in the decentralized training of nonsmooth neural networks. We propose a general framework that unifies various decentralized subgradient-based methods, such as decentralized stochastic subgradient descent (DSGD), DSGD with gradient-tracking technique (DSGD-T), and DSGD with momentum (DSGD-M). To establish the convergence properties of our proposed framework, we relate the discrete iterates to the trajectories of a continuous-time differential inclusion, which is assumed to have a coercive Lyapunov function with a stable set A. We prove the asymptotic convergence of the iterates to the stable set A with sufficiently small and diminishing step-sizes. These results provide first convergence guarantees for some well-recognized of decentralized stochastic subgradient-based methods without Clarke regularity of the objective function. Preliminary numerical experiments demonstrate that our proposed framework yields highly efficient decentralized stochastic subgradient-based methods with convergence guarantees in the training of nonsmooth neural networks.