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A Continuous-Time Analysis of Distributed Stochastic Gradient.

Nicholas M Boffi1, Jean-Jacques E Slotine2

  • 1John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, U.S.A. boffi@g.harvard.edu.

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Synchronization in distributed stochastic gradient algorithms, inspired by biological quorum sensing, reduces noise and improves convergence. This noise reduction enhances loss function smoothing and stabilizes training for complex objectives.

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Area of Science:

  • Optimization Algorithms
  • Distributed Machine Learning
  • Computational Neuroscience

Background:

  • Stochastic gradient descent (SGD) is fundamental to large-scale machine learning.
  • Distributed SGD algorithms face challenges with agent synchronization and noise.
  • Biological quorum sensing offers a model for agent synchronization via common signals.

Purpose of the Study:

  • To analyze the impact of synchronization on distributed stochastic gradient algorithms.
  • To quantify noise reduction in distributed agents through synchronization.
  • To investigate the convergence properties of synchronized distributed optimization.

Main Methods:

  • Analogy with biological quorum sensing for agent synchronization.
  • Mathematical analysis of convergence for strongly convex functions.
  • Numerical simulations on nonconvex objectives and convolutional neural networks (CIFAR-10).

Main Results:

  • Synchronization significantly reduces noise experienced by distributed agents and their spatial mean.
  • Noise reduction leads to less smoothing of the loss function in stochastic gradient approximation.
  • Coupling stabilizes higher noise levels and improves convergence in nonconvex objectives.
  • Elastic Averaging SGD (EASGD) exhibits a surprising regularizing property, even in non-distributed settings.

Conclusions:

  • Synchronization is a key mechanism for enhancing distributed stochastic gradient algorithms.
  • Quorum sensing-inspired algorithms and EASGD offer improved convergence and stability.
  • EASGD suggests potential for novel second-order optimization methods competitive with momentum.