标题： 随机时变网络上非光滑凸和凸凹问题的分布式优化 显示英文标题

标题： Stochastic Decentralized Optimization of Non-Smooth Convex and Convex-Concave Problems over Time-Varying Networks

摘要： 我们研究随时间变化的网络上的非光滑随机分布式优化问题，其中目标函数分布在各个节点上，网络连接可能间歇性出现或中断。 具体而言，我们考虑两种情况：(i) 随机非光滑（强）凸优化，以及 (ii) 随机非光滑（强）凸-（强）凹鞍点优化。 此类凸问题常见于深度神经网络训练，而鞍点问题在生成对抗网络（GANs）的训练等机器学习任务中起着核心作用。 先前的工作主要集中在光滑情况下，或者时间不变的网络场景中。 我们将现有理论扩展到更一般的非光滑和随机设置，在随时间变化的网络和鞍点问题上进行分析。 我们的分析建立了随机预言机调用次数和通信轮数的上界，与凸优化和鞍点优化问题的下界相匹配。 显示英文摘要

摘要： We study non-smooth stochastic decentralized optimization problems over time-varying networks, where objective functions are distributed across nodes and network connections may intermittently appear or break. Specifically, we consider two settings: (i) stochastic non-smooth (strongly) convex optimization, and (ii) stochastic non-smooth (strongly) convex-(strongly) concave saddle point optimization. Convex problems of this type commonly arise in deep neural network training, while saddle point problems are central to machine learning tasks such as the training of generative adversarial networks (GANs). Prior works have primarily focused on the smooth setting, or time-invariant network scenarios. We extend the existing theory to the more general non-smooth and stochastic setting over time-varying networks and saddle point problems. Our analysis establishes upper bounds on both the number of stochastic oracle calls and communication rounds, matching lower bounds for both convex and saddle point optimization problems.