Soft BIBD and Product Gradient Codes

TL;DR

This paper introduces new gradient coding schemes for distributed machine learning that are more flexible in system parameters while maintaining high robustness against slow or unresponsive machines.

Contribution

It proposes two novel constructions of gradient codes that extend BIBD-based codes to a wider range of parameters, improving practicality and performance.

Findings

Probabilistic construction relaxes BIBD constraints.

Kronecker product method creates new codes from existing ones.

Codes achieve comparable error performance with greater flexibility.

Abstract

Gradient coding is a coding theoretic framework to provide robustness against slow or unresponsive machines, known as stragglers, in distributed machine learning applications. Recently, Kadhe et al. proposed a gradient code based on a combinatorial design, called balanced incomplete block design (BIBD), which is shown to outperform many existing gradient codes in worst-case adversarial straggling scenarios. However, parameters for which such BIBD constructions exist are very limited. In this paper, we aim to overcome such limitations and construct gradient codes which exist for a wide range of system parameters while retaining the superior performance of BIBD gradient codes. Two such constructions are proposed, one based on a probabilistic construction that relax the stringent BIBD gradient code constraints, and the other based on taking the Kronecker product of existing gradient codes. The proposed gradient codes allow flexible choices of system parameters while retaining comparable error performance.