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A Distributed Algorithm for Measure-valued Optimization with Additive Objective

arXiv 2202.08930 ↗First posted 17 Feb 2022math.OC cs.LG cs.SYcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 18 of its 32 references that are in the map. First posted on arXiv 17 Feb 2022.

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References · 18

  1. 2018A Mean Field View of the Landscape of Two-Layers Neural Networkscited by 463
  2. 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 422
  3. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  4. 2020Variational Policy Gradient Method for Reinforcement Learning with General Utilitiescited by 108
  5. 2018Mean Field Analysis of Neural Networks: A Central Limit Theoremcited by 107
  6. 2021Large-Scale Wasserstein Gradient Flowscited by 76
  7. 2021Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networkscited by 53
  8. 2019Wasserstein Proximal Algorithms for the Schr"odinger Bridge Problem: Density Control with Nonlinear Driftcited by 50
  9. 2018Policy Optimization as Wasserstein Gradient Flowscited by 33
  10. 2015A Smoothed Dual Approach for Variational Wasserstein Problemscited by 29
  11. 2020Reflected Schr"odinger Bridge: Density Control with Path Constraintscited by 22
  12. 2017Gradient Flows in Filtering and Fisher-Rao Geometrycited by 12
6 more
  1. 2019Probability Functional Descent: A Unifying Perspective on GANs, Variational Inference, and Reinforcement Learningcited by 11
  2. 2019Gradient Flow Algorithms for Density Propagation in Stochastic Systemscited by 10
  3. 2016Generalized Sinkhorn iterations for regularizing inverse problems using optimal mass transportcited by 7
  4. 2018Proximal Recursion for Solving the Fokker-Planck Equationcited by 7
  5. 2017Gradient Flows in Uncertainty Propagation and Filtering of Linear Gaussian Systemscited by 6
  6. 2019Proximal Recursion for the Wonham Filtercited by 4

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