Generalized EXTRA stochastic gradient Langevin dynamics

Mert Gürbüzbalaban; Mohammad Rafiqul Islam; Xiaoyu Wang; Lingjiong Zhu

Preprint, 2024

Generalized EXTRA stochastic gradient Langevin dynamics

Mert Gürbüzbalaban, Mohammad Rafiqul Islam, Xiaoyu Wang, Lingjiong Zhu

arXiv preprint, 2024.

arXiv:2412.01993

In brief

Decentralized stochastic gradient Langevin dynamics lets agents sample a posterior over a network without sharing data, but network effects bias the samples, most visibly with full-batch gradients. Borrowing the EXTRA correction from decentralized optimization removes that bias: the method converges to the target posterior in 2-Wasserstein distance under strong convexity and smoothness, and outperforms plain decentralized SGLD when communication is constrained.

Topics

Sampling & Langevin algorithms Distributed & decentralized learning

Cite

@misc{gurbuzbalaban2024extra,
  title   = {Generalized EXTRA stochastic gradient Langevin dynamics},
  author  = {Mert Gürbüzbalaban and Mohammad Rafiqul Islam and Xiaoyu Wang and Lingjiong Zhu},
  year    = {2024},
  howpublished = {arXiv preprint arXiv:2412.01993},
}