We propose Decentralized Proximal Stochastic Gradient Langevin Dynamics (DE-PSGLD), a decentralized Markov chain Monte Carlo (MCMC) algorithm for sampling from a log-concave probability distribution constrained to a convex domain. Constraints are enforced through a shared proximal regularization based on the Moreau-Yosida envelope, enabling unconstrained updates while preserving consistency with the target constrained posterior. We establish non-asymptotic convergence guarantees in the 2-Wasserstein distance for both individual agent iterates and their network averages. Our analysis shows that DE-PSGLD converges to a regularized Gibbs distribution and quantifies the bias introduced by the proximal approximation. We evaluate DE-PSGLD for different sampling problems on synthetic and real datasets. As the first decentralized approach for constrained domains, our algorithm exhibits fast posterior concentration and high predictive accuracy.

翻译：我们提出去中心化近端随机梯度朗之万动力学（DE-PSGLD），这是一种分布式马尔可夫链蒙特卡洛（MCMC）算法，用于从约束在凸域上的对数凹概率分布中进行采样。约束通过基于Moreau-Yosida包络的共享近端正则化来强制执行，从而在保持与目标约束后验一致性的同时实现无约束更新。我们在2-Wasserstein距离上为单个智能体迭代及其网络平均值建立了非渐近收敛保证。我们的分析表明，DE-PSGLD收敛到正则化吉布斯分布，并量化了近端近似引入的偏差。我们在合成数据集和真实数据集上针对不同采样问题评估了DE-PSGLD。作为首个针对约束域的去中心化方法，我们的算法展现出快速的后验集中性和高预测精度。