On Gradient Coding With Partial Recovery

• Published in: IEEE transactions on communications Vol. 71; no. 2; pp. 644 - 657
• Main Authors: Sarmasarkar, Sahasrajit, Lalitha, V., Karamchandani, Nikhil
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Codes; Coding; coding theory; Communication; Computation; Distributed computation; Distributed databases; Encoding; information theory; Load modeling; Lower bounds; Machine learning; Polynomials; Simulation; straggler mitigation; Task analysis
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2022.3230779

We consider a generalization of the gradient coding framework where a dataset is divided across <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> workers and each worker transmits to a master node one or more linear combinations of the gradients over its assigned data subsets. Unlike the conventional framework which requires the master node to recover the sum of the gradients over all the data subsets in the presence of straggler workers, we relax the goal to computing the sum of at least some <inline-formula> <tex-math notation="LaTeX">\alpha </tex-math></inline-formula> fraction of the gradients. We begin by deriving a lower bound on the computation load of any scheme and also propose two strategies which achieve this lower bound, albeit at the cost of high communication load and a number of data partitions which can be polynomial in <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>. We then propose schemes based on cyclic assignment which utilize <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> data partitions and have a lower communication load. When each worker transmits a single linear combination, we prove lower bounds on the computation load of any scheme using <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> data partitions. Finally, we describe a class of schemes which achieve different intermediate operating points for the computation and communication load and provide simulation results to demonstrate the empirical performance of our schemes.