Straggler Mitigation through Unequal Error Protection for Distributed Matrix Multiplication

TL;DR

This paper introduces a novel approach using Unequal Error Protection codes to mitigate stragglers in distributed matrix multiplication, improving resilience by prioritizing larger norm sub-blocks, validated through theoretical analysis and neural network training experiments.

Contribution

It proposes UEP coding for distributed matrix multiplication, emphasizing protection based on sub-block norms, and analyzes its performance compared to equal error protection schemes.

Findings

UEP codes improve resilience against stragglers in matrix multiplication.

Theoretical analysis shows UEP outperforms equal error protection.

Application to DNN training demonstrates trade-offs between precision and computation time.

Abstract

Large-scale machine learning and data mining methods routinely distribute computations across multiple agents to parallelize processing. The time required for computation at the agents is affected by the availability of local resources giving rise to the "straggler problem" in which the computation results are held back by unresponsive agents. For this problem, linear coding of the matrix sub-blocks can be used to introduce resilience toward straggling. The Parameter Server (PS) utilizes a channel code and distributes the matrices to the workers for multiplication. It then produces an approximation to the desired matrix multiplication using the results of the computations received at a given deadline. In this paper, we propose to employ Unequal Error Protection (UEP) codes to alleviate the straggler problem. The resiliency level of each sub-block is chosen according to its norm as blocks with larger norms have higher effects on the result of the matrix multiplication. We validate the effectiveness of our scheme both theoretically and through numerical evaluations. We derive a theoretical characterization of the performance of UEP using random linear codes, and compare it the case of equal error protection. We also apply the proposed coding strategy to the computation of the back-propagation step in the training of a Deep Neural Network (DNN), for which we investigate the fundamental trade-off between precision and the time required for the computations.