A Hybrid-Order Distributed SGD Method for Non-Convex Optimization to Balance Communication Overhead, Computational Complexity, and Convergence Rate

03/27/2020
by   Naeimeh Omidvar, et al.
18

In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iteration of the algorithm, the worker nodes calculate and communicate some scalers, that are the directional derivatives of the sample functions in some pre-shared directions. However, to maintain accuracy, after every specific number of iterations, they communicate the vectors of stochastic gradients. To reduce the computational complexity in each iteration, the worker nodes approximate the directional derivatives with zeroth-order stochastic gradient estimation, by performing just two function evaluations rather than computing a first-order gradient vector. The proposed method highly improves the convergence rate of the zeroth-order methods, guaranteeing order-wise faster convergence. Moreover, compared to the famous communication-efficient methods of model averaging (that perform local model updates and periodic communication of the gradients to synchronize the local models), we prove that for the general class of non-convex stochastic problems and with reasonable choice of parameters, the proposed method guarantees the same orders of communication load and convergence rate, while having order-wise less computational complexity. Experimental results on various learning problems in neural networks applications demonstrate the effectiveness of the proposed approach compared to various state-of-the-art distributed SGD methods.

READ FULL TEXT
06/11/2020

STL-SGD: Speeding Up Local SGD with Stagewise Communication Period

Distributed parallel stochastic gradient descent algorithms are workhors...
05/30/2019

On the Convergence of Memory-Based Distributed SGD

Distributed stochastic gradient descent (DSGD) has been widely used for ...
07/20/2018

signProx: One-Bit Proximal Algorithm for Nonconvex Stochastic Optimization

Stochastic gradient descent (SGD) is one of the most widely used optimiz...
02/16/2021

IntSGD: Floatless Compression of Stochastic Gradients

We propose a family of lossy integer compressions for Stochastic Gradien...
02/22/2022

Asynchronous Fully-Decentralized SGD in the Cluster-Based Model

This paper presents fault-tolerant asynchronous Stochastic Gradient Desc...
02/05/2022

Distributed Learning With Sparsified Gradient Differences

A very large number of communications are typically required to solve di...
09/27/2018

The Convergence of Sparsified Gradient Methods

Distributed training of massive machine learning models, in particular d...