  One of the major challenges in using distributed learning to train
complicated models with large data sets is to deal with stragglers effect. As a
solution, coded computation has been recently proposed to efficiently add
redundancy to the computation tasks. In this technique, coding is used across
data sets, and computation is done over coded data, such that the results of an
arbitrary subset of worker nodes with a certain size are enough to recover the
final results. The major challenges with those approaches are (1) they are
limited to polynomial function computations, (2) the size of the subset of
servers that we need to wait for grows with the multiplication of the size of
the data set and the model complexity (the degree of the polynomial), which can
be prohibitively large, (3) they are not numerically stable for computation
over real numbers. In this paper, we propose Berrut Approximated Coded
Computing (BACC), as an alternative approach, which is not limited to
polynomial function computation. In addition, the master node can approximately
calculate the final results, using the outcomes of any arbitrary subset of
available worker nodes. The approximation approach is proven to be numerically
stable with low computational complexity. In addition, the accuracy of the
approximation is established theoretically and verified by simulation results
in different settings such as distributed learning problems. In particular,
BACC is used to train a deep neural network on a cluster of servers, which
outperforms repetitive computation (repetition coding) in terms of the rate of
convergence.
