Approximate Gradient Coding for Distributed Learning with Heterogeneous Stragglers

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 computational 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.