# Wasserstein Consensus ADMM

arXiv: https://arxiv.org/abs/2309.07351 · HTML: https://mlsanity.com/paper/2309.07351/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2023.

## Built on by (most cited first, 1 of 1)

- [Learning Concave Bid Shading Strategies in Online Auctions via Measure-valued Proximal Optimization](https://mlsanity.com/paper/2509.10693/) (2025)

## Abstract (arXiv)

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.