Decentralized Proximal Stochastic Gradient Langevin Dynamics

• URL: http://arxiv.org/abs/2605.00723v1
• Date: Fri, 01 May 2026 15:11:06 GMT
• Title: Decentralized Proximal Stochastic Gradient Langevin Dynamics
• Abstract summary: Decentralized Proximal Gradient Langevin Dynamics (DE-PSGLD) for sampling from a log-concave probability distribution constrained to a convex domain.<n>As the first decentralized approach for constrained domains, our algorithm exhibits fast posterior concentration and high predictive accuracy.
• Score: 4.385194124090593
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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