Gradient Coding from Cyclic MDS Codes and Expander Graphs

TL;DR

This paper introduces novel gradient coding methods using cyclic MDS codes and expander graphs to mitigate stragglers in distributed learning, enabling efficient approximate gradients with faster convergence and reduced computation.

Contribution

It presents new gradient coding schemes based on classical coding theory and expander graphs, including an approximate variant that balances accuracy and computational efficiency.

Findings

Cyclic MDS codes outperform existing solutions in certain parameter ranges.

Expander graph-based codes enable efficient approximate gradient computation.

Experimental results show close generalization error to full gradients with less computation.

Abstract

Gradient coding is a technique for straggler mitigation in distributed learning. In this paper we design novel gradient codes using tools from classical coding theory, namely, cyclic MDS codes, which compare favorably with existing solutions, both in the applicable range of parameters and in the complexity of the involved algorithms. Second, we introduce an approximate variant of the gradient coding problem, in which we settle for approximate gradient computation instead of the exact one. This approach enables graceful degradation, i.e., the $\ell_2$ error of the approximate gradient is a decreasing function of the number of stragglers. Our main result is that normalized adjacency matrices of expander graphs yield excellent approximate gradient codes, which enable significantly less computation compared to exact gradient coding, and guarantee faster convergence than trivial solutions under standard assumptions. We experimentally test our approach on Amazon EC2, and show that the generalization error of approximate gradient coding is very close to the full gradient while requiring significantly less computation from the workers.