Variants on Block Design Based Gradient Codes for Adversarial Stragglers

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 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. Theoretical error bounds for worst-case adversarial straggling scenarios are derived. Simulations show that the proposed constructions can outperform existing gradient codes with similar redundancy per data piece.