Distributed Newton Can Communicate Less and Resist Byzantine Workers

TL;DR

This paper introduces COMRADE, a communication-efficient and Byzantine-resilient distributed second order optimization algorithm that reduces communication rounds and filters out malicious workers, with proven convergence and empirical validation.

Contribution

The paper presents COMRADE, a novel second order distributed optimization method that is both communication-efficient and robust against Byzantine failures, addressing a gap in existing algorithms.

Findings

COMRADE achieves linear-quadratic convergence rate.

It reduces communication to once per iteration per worker.

The algorithm effectively filters Byzantine workers, maintaining accuracy.

Abstract

We develop a distributed second order optimization algorithm that is communication-efficient as well as robust against Byzantine failures of the worker machines. We propose COMRADE (COMunication-efficient and Robust Approximate Distributed nEwton), an iterative second order algorithm, where the worker machines communicate only once per iteration with the center machine. This is in sharp contrast with the state-of-the-art distributed second order algorithms like GIANT [34] and DINGO[7], where the worker machines send (functions of) local gradient and Hessian sequentially; thus ending up communicating twice with the center machine per iteration. Moreover, we show that the worker machines can further compress the local information before sending it to the center. In addition, we employ a simple norm based thresholding rule to filter-out the Byzantine worker machines. We establish the linear-quadratic rate of convergence of COMRADE and establish that the communication savings and Byzantine resilience result in only a small statistical error rate for arbitrary convex loss functions. To the best of our knowledge, this is the first work that addresses the issue of Byzantine resilience in second order distributed optimization. Furthermore, we validate our theoretical results with extensive experiments on synthetic and benchmark LIBSVM [5] data-sets and demonstrate convergence guarantees.