Balancing Communication and Computation in Distributed Optimization

Albert S. Berahas, Raghu Bollapragada, Nitish Shirish Keskar, Ermin Wei*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Methods for distributed optimization have received significant attention in recent years owing to their wide applicability in various domains including machine learning, robotics, and sensor networks. A distributed optimization method typically consists of two key components: communication and computation. More specifically, at every iteration (or every several iterations) of a distributed algorithm, each node in the network requires some form of information exchange with its neighboring nodes (communication) and the computation step related to a (sub)-gradient (computation). The standard way of judging an algorithm via only the number of iterations overlooks the complexity associated with each iteration. Moreover, various applications deploying distributed methods may prefer a different composition of communication and computation. Motivated by this discrepancy, in this paper, we propose an adaptive cost framework that adjusts the cost measure depending on the features of various applications. We present a flexible algorithmic framework, where communication and computation steps are explicitly decomposed to enable algorithm customization for various applications. We apply this framework to the well-known distributed gradient descent (DGD) method, and show that the resulting customized algorithms, which we call DGDt, NEAR-DGDt, and NEAR-DGD+, compare favorably to their base algorithms, both theoretically and empirically. The proposed NEAR-DGD+ algorithm is an exact first-order method where the communication and computation steps are nested, and when the number of communication steps is adaptively increased, the method converges to the optimal solution. We test the performance and illustrate the flexibility of the methods, as well as practical variants, on quadratic functions and classification problems that arise in machine learning, in terms of iterations, gradient evaluations, communications, and the proposed cost framework.

Original languageEnglish (US)
Article number8528465
Pages (from-to)3141-3155
Number of pages15
JournalIEEE Transactions on Automatic Control
Volume64
Issue number8
DOIs
StatePublished - Aug 2019

Keywords

  • Communication
  • distributed optimization
  • network optimization
  • optimization algorithms

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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