一种用于约束域采样的去中心化采样算法，收敛快且精度高。
Decentralized Proximal Stochastic Gradient Langevin Dynamics
- 通过共享的近似正则化实现约束保持，支持无约束更新
- 在2-Wasserstein距离下证明了非渐近收敛性，偏差可量化
- 首个针对约束域的去中心化采样方法，适合分布式贝叶斯推断
我们提出去中心化近端随机梯度Langevin动力学（DE-PSGLD），一种用于从凸域上的对数凹概率分布中采样的去中心化马尔可夫链蒙特卡罗（MCMC）算法。通过基于Moreau-Yosida包络的共享近端正则化强制约束，实现无约束更新的同时保持与目标约束后验的一致性。我们建立了个体智能体迭代和网络平均在2-Wasserstein距离下的非渐近收敛保证。分析表明，DE-PSGLD收敛至一个正则化的吉布斯分布，并量化了近端近似带来的偏差。我们在合成与真实数据集上评估了该算法在不同采样问题上的表现。作为首个面向约束域的去中心化方法，该算法表现出快速后验集中和高预测精度。
原文摘要 · Abstract (English)
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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