Wasserstein Consensus ADMM

Iman Nodozi; Abhishek Halder

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arXiv · 2309.07351

Wasserstein Consensus ADMM

Iman Nodozi·Abhishek Halder

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Abstract

We introduce Wasserstein consensus alternating direction method of multipliers (ADMM) and its entropic-regularized version: Sinkhorn consensus ADMM, to solve measure-valued optimization problems with convex additive objectives. Several problems of interest in stochastic prediction and learning can be cast in this form of measure-valued convex additive optimization. The proposed algorithm generalizes a variant of the standard Euclidean ADMM to the space of probability measures but departs significantly from its Euclidean counterpart. In particular, we derive a two layer ADMM algorithm wherein the outer layer is a variant of consensus ADMM on the space of probability measures while the inner layer is a variant of Euclidean ADMM. The resulting computational framework is particularly suitable for solving Wasserstein gradient flows via distributed computation. We demonstrate the proposed framework using illustrative numerical examples.

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BibTeX RIS

Iman Nodozi, Abhishek Halder. 2023-09-13. Wasserstein Consensus ADMM. https://arxiv.org/abs/2309.07351

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