Coded Distributed Computing with Partial Recovery

Abstract

Coded computation techniques provide robustness against straggling workers in distributed computing. However, most of the existing schemes require exact provisioning of the straggling behaviour and ignore the computations carried out by straggling workers. Moreover, these schemes are typically designed to recover the desired computation results accurately, while in many machine learning and iterative optimization algorithms, faster approximate solutions are known to result in an improvement in the overall convergence time. In this paper, we first introduce a novel coded matrix-vector multiplication scheme, called coded computation with partial recovery (CCPR), which benefits from the advantages of both coded and uncoded computation schemes, and reduces both the computation time and the decoding complexity by allowing a trade-off between the accuracy and the speed of computation. We then extend this approach to distributed implementation of more general computation tasks by proposing a coded communication scheme with partial recovery, where the results of subtasks computed by the workers are coded before being communicated. Numerical simulations on a large linear regression task confirm the benefits of the proposed distributed computation scheme with partial recovery in terms of the trade-off between the computation accuracy and latency.

On Gradient Coding with Partial Recovery

“…This is a different form of approximation as compared to that considered in previous works on gradient coding mentioned above and such forms of approximate gradient recovery have found application in distributed learning algorithms [15], [16]. A similar objective function was also studied recently in [12], [24], [25], where the goal was to design strategies which benefit from both uncoded and coded computing schemes, and extensive numerical simulations were done to illustrate the advantages of allowing partial recovery. Finally, we would like to point out that while [21] studied approximate gradient coding in terms of 2 error, their gradient code construction based on Batched Raptor codes can in fact be applied to the partial recovery framework being studied here as well.…”