Compression with Exact Error Distribution for Federated Learning

Mahmoud Hegazy (1) , Rémi Leluc (1) , Cheuk Ting Li (2) , Aymeric Dieuleveut (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 CUHK - City University of Hong Kong [Hong Kong]

Compression schemes have been extensively used in Federated Learning (FL) to reduce the communication cost of distributed learning. While most approaches rely on a bounded variance assumption of the noise produced by the compressor, this paper investigates the use of compression and aggregation schemes that produce a specific error distribution, e.g., Gaussian or Laplace, on the aggregated data. We present and analyze different aggregation schemes based on layered quantizers achieving exact error distribution. We provide different methods to leverage the proposed compression schemes to obtain compression-for-free in differential privacy applications. Our general compression methods can recover and improve standard FL schemes with Gaussian perturbations such as Langevin dynamics and randomized smoothing.

Domains: Machine Learning [stat.ML]; Machine Learning [cs.LG]

Mahmoud Hegazy, Rémi Leluc, Cheuk Ting Li, Aymeric Dieuleveut. Compression with Exact Error Distribution for Federated Learning. International Conference on Artificial Intelligence and Statistics, May 2024, Valencia (Espagne), Spain. pp.613-621. ⟨hal-04554506⟩