Gradient Coding with Iterative Block Leverage Score Sampling

TL;DR

This paper introduces a novel iterative block leverage score sampling method for gradient coding in distributed linear regression, unifying randomized linear algebra with coded computing to improve efficiency and robustness.

Contribution

It generalizes leverage score sampling for distributed settings, enabling approximate coded computing without random projections, and incorporates weighting for enhanced compression.

Findings

Achieves approximation guarantees via induced sampling distribution.

Unifies randomized linear algebra with coded computing.

Provides an iterative sketching approach for linear regression.

Abstract

We generalize the leverage score sampling sketch for $\ell_2$-subspace embeddings, to accommodate sampling subsets of the transformed data, so that the sketching approach is appropriate for distributed settings. This is then used to derive an approximate coded computing approach for first-order methods; known as gradient coding, to accelerate linear regression in the presence of failures in distributed computational networks, \textit{i.e.} stragglers. We replicate the data across the distributed network, to attain the approximation guarantees through the induced sampling distribution. The significance and main contribution of this work, is that it unifies randomized numerical linear algebra with approximate coded computing, while attaining an induced $\ell_2$-subspace embedding through uniform sampling. The transition to uniform sampling is done without applying a random projection, as in the case of the subsampled randomized Hadamard transform. Furthermore, by incorporating this technique to coded computing, our scheme is an iterative sketching approach to approximately solving linear regression. We also propose weighting when sketching takes place through sampling with replacement, for further compression.