Client-only Distributed Markov Chain Monte Carlo Sampling over a Network

Bo Yuan, Jiaojiao Fan, Jiaming Liang, Yongxin Chen

Abstract:

We aim to sample from a target
$\exp\left(-\sum_{i=1}^n f_i(x|\mathcal{D}_i\right))$ where each client $f_i$ only has access to local data $\mathcal{D}_i$. We present a fully distributed Markov Chain Monte Carlo (MCMC) sampler that operates through client-to-client communication, eliminating the need for additional centralized servers. Unlike MCMC algorithms that rely on server-client structures, our proposed sampler is entirely distributed, enhancing security and robustness through decentralized communication.
In contrast to limited decentralized algorithms arising from Langevin dynamics, our sampler utilizes blocked Gibbs sampling on an augmented distribution. Furthermore, we establish a non-asymptotic analysis of our sampler, employing innovative techniques. This study contributes to one of the initial analyses of the non-asymptotic behavior of a fully distributed sampler arising from Gibbs sampling.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

Final revisions:
1. added additional experiments in Appendix A.6
2. expanded the discussion of differences from Yuan et al., 2023 in Appendix A.7
3. strengthened the comparison to prior work in the Introduction
4. explicitly acknowledge in the algorithm section that Steps 2–4 are adapted from Yuan et al., 2023.
5. corrections on grammatical errors.

Assigned Action Editor: ~Alain_Durmus1

Submission Number: 4578