BM2: Coupled Schrödinger Bridge Matching

2024-09-14

arXiv.org

AI Summary

This work addresses the problem of dynamic distributional transport. We propose a non-iterative neural network learning framework for efficiently solving entropy-regularized optimal transport. Methodologically, we introduce the first end-to-end, iteration-free learning approach for the Schrödinger bridge—without requiring iterative optimization—and enforce consistency between forward and backward bridge processes via a coupling-matching mechanism. Neural parameterization is grounded in analytically tractable diffusion processes, and we design coupled losses together with dynamical constraints to faithfully model the bridge dynamics. Theoretically, we provide convergence analysis. Experiments demonstrate that our method significantly outperforms baselines on distribution alignment tasks, achieving superior training efficiency, strong generalization across diverse distributions, and enhanced numerical stability.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Distributed Machine Learning & Federated Learning
• Planning, Routing, and Scheduling: Planning/Scheduling and Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

A Schr""{o}dinger bridge establishes a dynamic transport map between two target distributions via a reference process, simultaneously solving an associated entropic optimal transport problem. We consider the setting where samples from the target distributions are available, and the reference diffusion process admits tractable dynamics. We thus introduce Coupled Bridge Matching (BM$^2$), a simple non-iterative approach for learning Schr""{o}dinger bridges with neural networks. A preliminary theoretical analysis of the convergence properties of BM$^2$ is carried out, supported by numerical experiments that demonstrate the effectiveness of our proposal.

Problem

• Data Distribution
• Learning Algorithm
• Inter-distribution Relationship

Innovation

• Coupled Schrodinger Bridge Matching
• neural networks
• data distribution learning