Robust Gradient Descent via Moment Encoding with LDPC Codes

TL;DR

This paper introduces a novel distributed gradient descent method that encodes data moments with LDPC codes, providing robustness against stragglers and offering convergence guarantees, outperforming existing schemes.

Contribution

It proposes encoding data moments with LDPC codes for distributed gradient descent, enabling automatic adjustment to stragglers and theoretical convergence guarantees.

Findings

LDPC-based encoding improves robustness to stragglers.

The method converges similarly to stochastic gradient descent.

Experimental results show superior performance over existing schemes.

Abstract

This paper considers the problem of implementing large-scale gradient descent algorithms in a distributed computing setting in the presence of {\em straggling} processors. To mitigate the effect of the stragglers, it has been previously proposed to encode the data with an erasure-correcting code and decode at the master server at the end of the computation. We, instead, propose to encode the second-moment of the data with a low density parity-check (LDPC) code. The iterative decoding algorithms for LDPC codes have very low computational overhead and the number of decoding iterations can be made to automatically adjust with the number of stragglers in the system. We show that for a random model for stragglers, the proposed moment encoding based gradient descent method can be viewed as the stochastic gradient descent method. This allows us to obtain convergence guarantees for the proposed solution. Furthermore, the proposed moment encoding based method is shown to outperform the existing schemes in a real distributed computing setup.