Does Worst-Performing Agent Lead the Pack? Analyzing Agent Dynamics in Unified Distributed SGD
Keywords: Distributed Optimization, Agent Dynamics, Federated Learning, Central Limit Theorem, Efficient Sampling
TL;DR: We provide an asymptotic analysis of the Unified Distributed SGD, including decentralized SGD and various Federated Learning algorithms, to study the impact of agents' sampling strategies on the overall convergence of the large-scale system.
Abstract: Distributed learning is essential to train machine learning algorithms across *heterogeneous* agents while maintaining data privacy. We conduct an asymptotic analysis of Unified Distributed SGD (UD-SGD), exploring a variety of communication patterns, including decentralized SGD and local SGD within Federated Learning (FL), as well as the increasing communication interval in the FL setting. In this study, we assess how different sampling strategies, such as *i.i.d.* sampling, shuffling, and Markovian sampling, affect the convergence speed of UD-SGD by considering the impact of agent dynamics on the limiting covariance matrix as described in the Central Limit Theorem (CLT). Our findings not only support existing theories on linear speedup and asymptotic network independence, but also theoretically and empirically show how efficient sampling strategies employed by individual agents contribute to overall convergence in UD-SGD. Simulations reveal that a few agents using highly efficient sampling can achieve or surpass the performance of the majority employing moderately improved strategies, providing new insights beyond traditional analyses focusing on the worst-performing agent.
Primary Area: Learning theory
Submission Number: 1370
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