Communication-efficient distributed eigenspace estimation with arbitrary node failures

TL;DR

This paper introduces a distributed eigenspace estimation algorithm resilient to arbitrary node failures, including errors, outliers, and adversarial responses, maintaining near-optimal performance.

Contribution

It presents a novel eigenspace estimator that is robust to arbitrary node failures in distributed systems, extending previous methods to more adversarial scenarios.

Findings

Matches the performance of non-robust estimators up to an additive error

Handles arbitrary node responses including corrupted and adversarial data

Effective in distributed environments with silent or soft errors

Abstract

We develop an eigenspace estimation algorithm for distributed environments with arbitrary node failures, where a subset of computing nodes can return structurally valid but otherwise arbitrarily chosen responses. Notably, this setting encompasses several important scenarios that arise in distributed computing and data-collection environments such as silent/soft errors, outliers or corrupted data at certain nodes, and adversarial responses. Our estimator builds upon and matches the performance of a recently proposed non-robust estimator up to an additive $\tilde{O}(\sigma \sqrt{\alpha})$ error, where $\sigma^2$ is the variance of the existing estimator and $\alpha$ is the fraction of corrupted nodes.