Johnson-Lindenstrauss transforms improve robust distributed optimization
On Johnson-Lindenstrauss Transforms for Byzantine-Robust Optimization
Machine Learning
Summary
Large-scale machine learning requires splitting work across many computers that must talk to each other efficiently. One challenge is that some computers might send wrong or malicious messages, called Byzantine faults. The authors show how a mathematical technique called the Johnson-Lindenstrauss transform can help detect and reduce the influence of these bad messages by preserving important geometric information when compressing data. They support their idea both with math proofs and experiments.
What this means in practice
- •For distributed machine learning engineers: Reduce communication cost and improve fault tolerance in large-scale training by weighting updates with compressed gradients preserving alignment.
- •For data center network schedulers: Optimize bandwidth allocation by enabling reliable aggregation of worker nodes' updates even with some faulty or malicious nodes.
Authors
Aleksandr Shestakov, Vladimir Aletov, Aleksandr Beznosikov
Abstract
The growing scale of data and models in machine learning calls for efficient optimization methods. Distributed optimization addresses this challenge, with compression mechanisms helping to reduce communication costs. A classical tool for dimensionality reduction is the Johnson-Lindenstrauss (JL) transform, which is simple to implement and offers strong geometric guarantees. In particular, JL transforms approximately preserve inner products and pairwise distances between vectors with high probability. In this paper, we exploit this property in Byzantine-robust optimization, where worker messages are weighted according to their alignment with a trusted reference gradient. We further support our theoretical findings with experimental results.