Accelerated Gossip via Stochastic Heavy Ball Method

TL;DR

This paper demonstrates how the stochastic heavy ball method can be interpreted as a randomized gossip algorithm, introducing new protocols for distributed consensus with partial node communication, supported by numerical experiments.

Contribution

It connects the stochastic heavy ball method to gossip algorithms and proposes novel protocols for average consensus with partial node updates.

Findings

Protocols improve efficiency in wireless sensor networks

Partial communication reduces bandwidth usage

Numerical results show protocol benefits

Abstract

In this paper we show how the stochastic heavy ball method (SHB) -- a popular method for solving stochastic convex and non-convex optimization problems --operates as a randomized gossip algorithm. In particular, we focus on two special cases of SHB: the Randomized Kaczmarz method with momentum and its block variant. Building upon a recent framework for the design and analysis of randomized gossip algorithms, [Loizou Richtarik, 2016] we interpret the distributed nature of the proposed methods. We present novel protocols for solving the average consensus problem where in each step all nodes of the network update their values but only a subset of them exchange their private values. Numerical experiments on popular wireless sensor networks showing the benefits of our protocols are also presented.