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Oral
Gradient Coding from Cyclic MDS Codes and Expander Graphs
Netanel Raviv · Rashish Tandon · Alexandros Dimakis · Itzhak Tamo

Thu Jul 12 05:20 AM -- 05:30 AM (PDT) @ A9
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 favourably 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 the normalized adjacency matrix of an expander graph can yield excellent approximate gradient codes, and that this approach allows us to perform significantly less computation compared to exact gradient coding. 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.

#### Author Information

##### Alex Dimakis (UT Austin)

Alex Dimakis is an Associate Professor at the Electrical and Computer Engineering department, University of Texas at Austin. He received his Ph.D. in electrical engineering and computer sciences from UC Berkeley. He received an ARO young investigator award in 2014, the NSF Career award in 2011, a Google faculty research award in 2012 and the Eli Jury dissertation award in 2008. He is the co-recipient of several best paper awards including the joint Information Theory and Communications Society Best Paper Award in 2012. His research interests include information theory, coding theory and machine learning.