Approximate Gradient Coding for Distributed Learning with Heterogeneous Stragglers

TL;DR

This paper introduces an optimized gradient coding scheme for distributed learning that effectively handles heterogeneous stragglers, reducing redundancy and accelerating convergence.

Contribution

It formulates a novel optimization framework with closed-form solutions for encoding and decoding, addressing heterogeneity in straggler models and improving upon existing methods.

Findings

Significantly reduces the impact of stragglers in distributed learning.

Accelerates convergence compared to existing gradient coding methods.

Provides theoretical analysis of convergence behavior for convex and smooth functions.

Abstract

In this paper, we propose an optimally structured gradient coding scheme to mitigate the straggler problem in distributed learning. Conventional gradient coding methods often assume homogeneous straggler models or rely on excessive data replication, limiting performance in real-world heterogeneous systems. To address these limitations, we formulate an optimization problem minimizing residual error while ensuring unbiased gradient estimation by explicitly considering individual straggler probabilities. We derive closed-form solutions for optimal encoding and decoding coefficients via Lagrangian duality and convex optimization, and propose data allocation strategies that reduce both redundancy and computation load. We also analyze convergence behavior for $\lambda$-strongly convex and $\mu$-smooth loss functions. Numerical results show that our approach significantly reduces the impact of stragglers and accelerates convergence compared to existing methods.