# Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers

arXiv: https://arxiv.org/abs/2401.15838 · HTML: https://mlsanity.com/paper/2401.15838/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 23 of 23)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Federated Learning via Posterior Averaging: A New Perspective and Practical Algorithms](https://mlsanity.com/paper/2010.05273/) (2020)
- [On the Linear Convergence of the ADMM in Decentralized Consensus Optimization](https://mlsanity.com/paper/1307.5561/) (2013)
- [Split-and-augmented Gibbs sampler - Application to large-scale inference problems](https://mlsanity.com/paper/1804.05809/) (2018)
- [Proximal Markov chain Monte Carlo algorithms](https://mlsanity.com/paper/1306.0187/) (2013)
- [Asymptotically Exact, Embarrassingly Parallel MCMC](https://mlsanity.com/paper/1311.4780/) (2013)
- [Efficient MCMC Sampling with Dimension-Free Convergence Rate using ADMM-type Splitting](https://mlsanity.com/paper/1905.11937/) (2019)
- [Decentralized Stochastic Gradient Langevin Dynamics and Hamiltonian Monte Carlo](https://mlsanity.com/paper/2007.00590/) (2020)
- [Stochastic Proximal Langevin Algorithm: Potential Splitting and Nonasymptotic Rates](https://mlsanity.com/paper/1905.11768/) (2019)
- [DiNNO: Distributed Neural Network Optimization for Multi-Robot Collaborative Learning](https://mlsanity.com/paper/2109.08665/) (2021)
- [The Proximal Robbins-Monro Method](https://mlsanity.com/paper/1510.00967/) (2015)
- [On Convergence of Federated Averaging Langevin Dynamics](https://mlsanity.com/paper/2112.05120/) (2021)
- [Decentralized Bayesian Learning over Graphs](https://mlsanity.com/paper/1905.10466/) (2019)
- [Distributed Optimization Methods for Multi-Robot Systems: Part I -- A Tutorial](https://mlsanity.com/paper/2301.11313/) (2023)
- [Distributed Optimization Methods for Multi-Robot Systems: Part II -- A Survey](https://mlsanity.com/paper/2301.11361/) (2023)
- [Decentralized Bayesian Learning with Metropolis-Adjusted Hamiltonian Monte Carlo](https://mlsanity.com/paper/2107.07211/) (2021)
- [ELF: Federated Langevin Algorithms with Primal, Dual and Bidirectional Compression](https://mlsanity.com/paper/2303.04622/) (2023)
- [Stochastic Modified Equations for Continuous Limit of Stochastic ADMM](https://mlsanity.com/paper/2003.03532/) (2020)
- [A Decentralized Approach to Bayesian Learning](https://mlsanity.com/paper/2007.06799/) (2020)

## Abstract (arXiv)

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers, which is commonly used in the optimization literature due to its fast convergence. In contrast to distributed optimization, distributed sampling allows for uncertainty quantification in Bayesian inference tasks. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. For our theoretical results, we use convex optimization tools to establish a fundamental inequality on the generated local sample iterates. This inequality enables us to show convergence of the distribution associated with these iterates to the underlying target distribution in Wasserstein distance. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.