Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Jie Hu, Yi-Ting Ma, Do Young Eun

TL;DR

An asymptotic analysis of Unified Distributed SGD finds 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.

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.

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

TL;DR

An asymptotic analysis of Unified Distributed SGD finds 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.

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.
Paper Structure (25 sections, 14 theorems, 94 equations, 3 figures, 1 table)

This paper contains 25 sections, 14 theorems, 94 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Asymptotic Analysis of UD-SGD
  4. Experiments
  5. Conclusion
  6. Acknowledgments and Disclosure of Funding
  7. Discussion of \ref{['assumption:Decreasing step size and slowly increasing communication interval']}-ii)
  8. Suitable choices of $K_l$
  9. Practical implications of \ref{['assumption:Decreasing step size and slowly increasing communication interval']}-ii)
  10. Proof of \ref{['lemma:consensus']}
  11. Proof of \ref{['theorem: almost_sure_convergence']}
  12. Proof of \ref{['theorem: CLT_D-SGD']}
  13. Discussion about C1-C3
  14. Analysis of C4
  15. Analysis of C5
  16. ...and 10 more sections

Key Result

Lemma 3.1

Under Assumptions assumption:Regularity of the gradient, assumption:Decreasing step size and slowly increasing communication interval, assumption:Boundedness on model parameter and assumption:Contraction property of communication matrix, the consensus error $\theta_n^i \!-\! \theta_n$ diminishes to

Figures (3)

  • Figure 1: GD-SGD algorithm with a communication network of $N=5$ agents, each holding potentially distinct datasets; e.g., agent $j$ (in blue) samples $\mathcal{X}_j$i.i.d. and agent $i$ (in red) samples $\mathcal{X}_i$ via Markovian trajectory.
  • Figure 2: Binary classification problem. From left to right: (a) Impact of efficient sampling strategies on convergence. (b) Performance gains from partial adoption of efficient sampling. (c) Comparative advantage of SRRW over NBRW in a small subset of agents. (d) Asymptotic network independence of four algorithms under UD-SGD framework with fixed sampling strategy (shuffling, SRRW). (e) Different sampling strategies in the DSGD algorithm with time-varying topology (DSGD-VT). (f) Different sampling strategies in the DFL algorithm with increasing communication interval.
  • Figure 3: Image classification experiment. From left to right: (a) Comparison of various sampling strategies in image classification problem using $5$-layer neural network. (b) Train a $5$-layer CNN model with different number of total agents (clients) to show the linear speedup effect. (c) Train ResNet-$18$ model with different sampling strategies among $10$ agents with participation ratio $0.4$.

Theorems & Definitions (20)

  • Remark 1
  • Lemma 3.1
  • Theorem 3.2
  • Theorem 3.3
  • Remark 2
  • Remark 3
  • Corollary 3.4
  • Lemma B.1
  • proof : Proof of \ref{['lemma:boundedness_phi']}
  • Theorem C.1: Theorem 2 delyon1999convergence
  • ...and 10 more