Asynchronous Distributed Optimization with Redundancy in Cost Functions

by   Shuo Liu, et al.

This paper considers the problem of asynchronous distributed multi-agent optimization on server-based system architecture. In this problem, each agent has a local cost, and the goal for the agents is to collectively find a minimum of their aggregate cost. A standard algorithm to solve this problem is the iterative distributed gradient-descent (DGD) method being implemented collaboratively by the server and the agents. In the synchronous setting, the algorithm proceeds from one iteration to the next only after all the agents complete their expected communication with the server. However, such synchrony can be expensive and even infeasible in real-world applications. We show that waiting for all the agents is unnecessary in many applications of distributed optimization, including distributed machine learning, due to redundancy in the cost functions (or data). Specifically, we consider a generic notion of redundancy named (r,ϵ)-redundancy implying solvability of the original multi-agent optimization problem with ϵ accuracy, despite the removal of up to r (out of total n) agents from the system. We present an asynchronous DGD algorithm where in each iteration the server only waits for (any) n-r agents, instead of all the n agents. Assuming (r,ϵ)-redundancy, we show that our asynchronous algorithm converges to an approximate solution with error that is linear in ϵ and r. Moreover, we also present a generalization of our algorithm to tolerate some Byzantine faulty agents in the system. Finally, we demonstrate the improved communication efficiency of our algorithm through experiments on MNIST and Fashion-MNIST using the benchmark neural network LeNet.


page 1

page 2

page 3

page 4


Utilizing Redundancy in Cost Functions for Resilience in Distributed Optimization and Learning

This paper considers the problem of resilient distributed optimization a...

A Canonical Form for First-Order Distributed Optimization Algorithms

We consider the distributed optimization problem in which a network of a...

Approximate Byzantine Fault-Tolerance in Distributed Optimization

We consider the problem of Byzantine fault-tolerance in distributed mult...

Asynchronous Distributed Optimization with Randomized Delays

In this work, we study asynchronous finite sum minimization in a distrib...

DSPG: Decentralized Simultaneous Perturbations Gradient Descent Scheme

In this paper, we present an asynchronous approximate gradient method th...

Collective Online Learning via Decentralized Gaussian Processes in Massive Multi-Agent Systems

Distributed machine learning (ML) is a modern computation paradigm that ...

The END: Estimation Network Design for efficient distributed equilibrium seeking

Multi-agent decision problems are typically solved via distributed algor...