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Updated: Jul 27, 2025

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A Sharp Estimate on the Transient Time of Distributed Stochastic Gradient Descent.

Shi Pu1, Alex Olshevsky2, Ioannis Ch Paschalidis2

  • 1School of Data Science, Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen, China.

IEEE Transactions on Automatic Control
|June 7, 2023
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This study analyzes distributed stochastic gradient descent (DSGD) for network optimization with noisy data. DSGD achieves optimal convergence rates, with new findings on its transient time performance.

Keywords:
convex optimizationdistributed optimizationstochastic gradient descentstochastic programming

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Area of Science:

  • Optimization Theory
  • Distributed Systems
  • Machine Learning

Background:

  • Decentralized optimization problems involve minimizing average cost functions across networks.
  • Agents often rely on noisy gradient information for decision-making.
  • Distributed stochastic gradient descent (DSGD) is a key method for such scenarios.

Purpose of the Study:

  • To perform a non-asymptotic convergence analysis of DSGD.
  • To characterize the transient time for DSGD to reach its asymptotic convergence rate.
  • To establish the sharpness of the theoretical results through a constructed optimization problem.

Main Methods:

  • Non-asymptotic convergence analysis of DSGD.
  • Theoretical analysis for strongly convex and smooth objective functions.
  • Construction of a challenging optimization problem to validate theoretical bounds.

Main Results:

  • DSGD achieves an optimal network-independent convergence rate in expectation, comparable to centralized stochastic gradient descent (SGD).
  • The study quantifies the transient time required for DSGD to approach its asymptotic convergence rate.
  • A "hard" optimization problem demonstrates the sharpness of the derived convergence bounds.

Conclusions:

  • DSGD is an effective method for distributed optimization with noisy gradients.
  • The characterization of transient time provides crucial insights into DSGD's practical performance.
  • Theoretical results are validated by numerical experiments, confirming their tightness.