Redundancy Techniques for Straggler Mitigation in Distributed Optimization and Learning

TL;DR

This paper introduces a redundancy-based distributed optimization framework that mitigates straggler effects by encoding data with over-complete representations, ensuring convergence despite delays and node failures.

Contribution

It proposes a novel encoding scheme using equiangular tight frames and demonstrates convergence guarantees for various optimization algorithms under arbitrary delay patterns.

Findings

Redundancy encoding improves robustness against stragglers.

The method converges deterministically regardless of delay distributions.

Experimental results show performance gains over traditional strategies.

Abstract

Performance of distributed optimization and learning systems is bottlenecked by "straggler" nodes and slow communication links, which significantly delay computation. We propose a distributed optimization framework where the dataset is "encoded" to have an over-complete representation with built-in redundancy, and the straggling nodes in the system are dynamically left out of the computation at every iteration, whose loss is compensated by the embedded redundancy. We show that oblivious application of several popular optimization algorithms on encoded data, including gradient descent, L-BFGS, proximal gradient under data parallelism, and coordinate descent under model parallelism, converge to either approximate or exact solutions of the original problem when stragglers are treated as erasures. These convergence results are deterministic, i.e., they establish sample path convergence for arbitrary sequences of delay patterns or distributions on the nodes, and are independent of the tail behavior of the delay distribution. We demonstrate that equiangular tight frames have desirable properties as encoding matrices, and propose efficient mechanisms for encoding large-scale data. We implement the proposed technique on Amazon EC2 clusters, and demonstrate its performance over several learning problems, including matrix factorization, LASSO, ridge regression and logistic regression, and compare the proposed method with uncoded, asynchronous, and data replication strategies.