论文标题
具有添加剂目标的测量值优化的分布式算法
A Distributed Algorithm for Measure-valued Optimization with Additive Objective
论文作者
论文摘要
我们提出了一种分布式的非参数算法，用于解决添加目标的测量值优化问题。此类问题在随机学习和控制中的几种情况下出现，包括来自不符合的先验，平均现场神经网络学习和Wasserstein梯度流的Langevin采样。所提出的算法包括乘数的两层交替方向方法（ADMM）。外层ADMM将欧几里得共识ADMM概括为Wasserstein Consensus admm，并概括了其熵登记的版本sindhorn共识ADMM。事实证明，内层ADMM是标准欧几里得ADMM的特定实例。总体算法实现了在概率度量的歧视中梯度流的运算符。
We propose a distributed nonparametric algorithm for solving measure-valued optimization problems with additive objectives. Such problems arise in several contexts in stochastic learning and control including Langevin sampling from an unnormalized prior, mean field neural network learning and Wasserstein gradient flows. The proposed algorithm comprises a two-layer alternating direction method of multipliers (ADMM). The outer-layer ADMM generalizes the Euclidean consensus ADMM to the Wasserstein consensus ADMM, and to its entropy-regularized version Sinkhorn consensus ADMM. The inner-layer ADMM turns out to be a specific instance of the standard Euclidean ADMM. The overall algorithm realizes operator splitting for gradient flows in the manifold of probability measures.
