AAMAS Conference 2026 Conference Paper
Scalable Knothe--Rosenblatt-like Heuristic Transportation Plans for Imaging Problems
- Gennaro Auricchio
- Min Lin
- Lingxuan Zhou
- Zhaori Guo
- Zhongqi Cai
In this paper, we introduce a novel formalism for computing the Wasserstein Distance between any pair of probability distributions, 𝜇 and 𝜈. Standard approaches require solving a matching problem betweentwodiscretedistributions, whichbecomescomputationally expensiveasthedimensionalityincreases. Toaddressthischallenge, we propose a new family of heuristic transportation plans that extend the classic Knothe–Rosenblatt transport plan. Each heuristic plan is associated with a method for combining the two original measures into an intermediate measure, significantly reducing the number of variables required to characterise any transportation plan. Specifically, if the probability measures 𝜇 and𝜈 have supports consisting of 𝑁 and 𝑀 points, respectively, our approach reduces thenumberofvariablesfrom 𝑁 ×𝑀 tomin{𝑁, 𝑀}. Wedemonstrate that our method is particularly well-suited for defining a neural network to solve the optimal transport problem and validate our model through extensive numerical experiments.