# A continuous-time analysis of distributed stochastic gradient

arXiv: https://arxiv.org/abs/1812.10995 · HTML: https://mlsanity.com/paper/1812.10995/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2018.

## Built on by (most cited first, 4 of 4)

- [Generalization in Supervised Learning Through Riemannian Contraction](https://mlsanity.com/paper/2201.06656/) (2022)
- [A Contraction Theory Approach to Optimization Algorithms from Acceleration Flows](https://mlsanity.com/paper/2105.08832/) (2021)
- [Unlocking optimal batch size schedules using continuous-time control and perturbation theory](https://mlsanity.com/paper/2312.01898/) (2023)
- [Fusing Multiple Algorithms for Heterogeneous Online Learning](https://mlsanity.com/paper/2312.05432/) (2023)

## Abstract (arXiv)

We analyze the effect of synchronization on distributed stochastic gradient algorithms. By exploiting an analogy with dynamical models of biological quorum sensing - where synchronization between agents is induced through communication with a common signal - we quantify how synchronization can significantly reduce the magnitude of the noise felt by the individual distributed agents and by their spatial mean. This noise reduction is in turn associated with a reduction in the smoothing of the loss function imposed by the stochastic gradient approximation. Through simulations on model non-convex objectives, we demonstrate that coupling can stabilize higher noise levels and improve convergence. We provide a convergence analysis for strongly convex functions by deriving a bound on the expected deviation of the spatial mean of the agents from the global minimizer for an algorithm based on quorum sensing, the same algorithm with momentum, and the Elastic Averaging SGD (EASGD) algorithm. We discuss extensions to new algorithms that allow each agent to broadcast its current measure of success and shape the collective computation accordingly. We supplement our theoretical analysis with numerical experiments on convolutional neural networks trained on the CIFAR-10 dataset, where we note a surprising regularizing property of EASGD even when applied to the non-distributed case. This observation suggests alternative second-order in-time algorithms for non-distributed optimization that are competitive with momentum methods.