Gradient Coding from Cyclic MDS Codes and Expander Graphs

Netanel Raviv*, Itzhak Tamo, Rashish Tandon, Alexandros G. Dimakis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original language English 9216021 7475-7489 15 IEEE Transactions on Information Theory 66 12 https://doi.org/10.1109/TIT.2020.3029396 Published - Dec 2020