Communication-Efficient Approximate Gradient Coding

2026-03-23

AI Summary

This work addresses the efficiency bottleneck caused by straggler nodes in large-scale distributed learning by proposing a communication-efficient approximate gradient coding scheme. By leveraging structured sparse encoding matrices derived from bipartite graphs, combinatorial designs, and strongly regular graphs—combined with randomization techniques and algebraic constraints—the method achieves unbiased approximation of the true gradient while substantially reducing communication overhead at worker nodes. Theoretical analysis establishes tight upper and lower bounds on the approximation error and proves that the algorithm converges in expectation to a stationary point. Experimental results demonstrate the superiority of the proposed approach in terms of fault tolerance, communication efficiency, and convergence performance.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Large-scale distributed learning aims at minimizing a loss function $L$ that depends on a training dataset with respect to a $d$-length parameter vector. The distributed cluster typically consists of a parameter server (PS) and multiple workers. Gradient coding is a technique that makes the learning process resilient to straggling workers. It introduces redundancy within the assignment of data points to the workers and uses coding theoretic ideas so that the PS can recover $\nabla L$ exactly or approximately, even in the presence of stragglers. Communication-efficient gradient coding allows the workers to communicate vectors of length smaller than $d$ to the PS, thus reducing the communication time. While there have been schemes that address the exact recovery of $\nabla L$ within communication-efficient gradient coding, to the best of our knowledge the approximate variant has not been considered in a systematic manner. In this work we present constructions of communication-efficient approximate gradient coding schemes. Our schemes use structured matrices that arise from bipartite graphs, combinatorial designs and strongly regular graphs, along with randomization and algebraic constraints. We derive analytical upper bounds on the approximation error of our schemes that are tight in certain cases. Moreover, we derive a corresponding worst-case lower bound on the approximation error of any scheme. For a large class of our methods, under reasonable probabilistic worker failure models, we show that the expected value of the computed gradient equals the true gradient. This in turn allows us to prove that the learning algorithm converges to a stationary point over the iterations. Numerical experiments corroborate our theoretical findings.

Problem

• gradient coding
• communication efficiency
• straggler mitigation
• approximate gradient
• distributed learning

Innovation

• approximate gradient coding
• communication efficiency
• structured matrices
• straggler resilience
• convergence guarantee