Lagrange Coded Computing: Optimal Design for Resiliency, Security and Privacy

TL;DR

Lagrange Coded Computing (LCC) is a novel framework that enhances distributed computations by providing optimal resiliency against stragglers, security against malicious workers, and privacy of data, applicable to polynomial functions in machine learning.

Contribution

LCC introduces a new coded computing framework leveraging Lagrange polynomials, achieving optimal tradeoffs among resiliency, security, and privacy in distributed polynomial computations.

Findings

Achieves up to 13.43x speedup in distributed linear regression.

Provides optimal tradeoff between resiliency, security, and privacy.

Outperforms existing straggler mitigation strategies significantly.

Abstract

We consider a scenario involving computations over a massive dataset stored distributedly across multiple workers, which is at the core of distributed learning algorithms. We propose Lagrange Coded Computing (LCC), a new framework to simultaneously provide (1) resiliency against stragglers that may prolong computations; (2) security against Byzantine (or malicious) workers that deliberately modify the computation for their benefit; and (3) (information-theoretic) privacy of the dataset amidst possible collusion of workers. LCC, which leverages the well-known Lagrange polynomial to create computation redundancy in a novel coded form across workers, can be applied to any computation scenario in which the function of interest is an arbitrary multivariate polynomial of the input dataset, hence covering many computations of interest in machine learning. LCC significantly generalizes prior works to go beyond linear computations. It also enables secure and private computing in distributed settings, improving the computation and communication efficiency of the state-of-the-art. Furthermore, we prove the optimality of LCC by showing that it achieves the optimal tradeoff between resiliency, security, and privacy, i.e., in terms of tolerating the maximum number of stragglers and adversaries, and providing data privacy against the maximum number of colluding workers. Finally, we show via experiments on Amazon EC2 that LCC speeds up the conventional uncoded implementation of distributed least-squares linear regression by up to $13.43\times$, and also achieves a $2.36\times$-$12.65\times$ speedup over the state-of-the-art straggler mitigation strategies.