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Optimal Communication-Computation Trade-Off in Heterogeneous Gradient Coding | IEEE Journals & Magazine | IEEE Xplore

Optimal Communication-Computation Trade-Off in Heterogeneous Gradient Coding


Abstract:

Gradient coding allows a master node to derive the aggregate of the partial gradients, calculated by some worker nodes over the local data sets, with minimum communicatio...Show More

Abstract:

Gradient coding allows a master node to derive the aggregate of the partial gradients, calculated by some worker nodes over the local data sets, with minimum communication cost, and in the presence of stragglers. In this paper, for gradient coding with linear encoding, we characterize the optimum communication cost for heterogeneous distributed systems with arbitrary data placement, with s \in \mathbb {N} stragglers and a \in \mathbb {N} adversarial nodes. In particular, we show that the optimum communication cost, normalized by the size of the gradient vectors, is equal to (r-s-2a)^{-1} , where r \in \mathbb {N} is the minimum number that a data partition is replicated. In other words, the communication cost is determined by the data partition with the minimum replication, irrespective of the structure of the placement. The proposed achievable scheme also allows us to target the computation of a polynomial function of the aggregated gradient matrix. It also allows us to borrow some ideas from approximation computing and propose an approximate gradient coding scheme for the cases when the repetition in data placement is smaller than what is needed to meet the restriction imposed on communication cost or when the number of stragglers appears to be more than the presumed value in the system design.
Published in: IEEE Journal on Selected Areas in Information Theory ( Volume: 2, Issue: 3, September 2021)
Page(s): 1002 - 1011
Date of Publication: 03 June 2021
Electronic ISSN: 2641-8770

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