Does Worst-Performing Agent Lead the Pack? Analyzing Agent Dynamics in Unified Distributed SGD

TL;DR

This paper analyzes how different agent sampling strategies and dynamics influence the convergence of Unified Distributed SGD in distributed learning, revealing that a few highly efficient agents can significantly impact overall performance.

Contribution

It provides a theoretical and empirical analysis of agent dynamics and sampling strategies in UD-SGD, highlighting the influence of efficient agents on convergence beyond the worst-performing agent.

Findings

Efficient sampling strategies by some agents can improve overall convergence.

Theoretical support for linear speedup and network independence in UD-SGD.

Simulations show few agents can outperform many with moderate strategies.

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.