Feedback Schrödinger Bridge Matching

2024-10-17

arXiv.org

AI Summary

In distribution transport, diffusion-based bridge methods face a trade-off between scalability and optimal coupling estimation: unsupervised approaches are computationally prohibitive, while fully supervised ones rely on complete pairwise alignment labels—often unavailable in practice. To address this, we propose FSBM, a semi-supervised framework that learns transport maps between uncoupled distributions using only <8% pre-aligned samples as sparse state feedback. We introduce, for the first time, pairwise feedback into the Schrödinger bridge framework, formulating a generalized static entropic optimal transport model with a feedback-regularized objective; this is further dynamized to balance computational efficiency and weak supervision. Experiments demonstrate that FSBM significantly accelerates convergence and improves generalization, outperforming both fully unsupervised and fully supervised baselines across diverse matching tasks. FSBM establishes a new paradigm for efficient distribution transport under partial alignment.

Technology Category

• Machine Learning: Semi-Supervised Learning
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

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
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Recent advancements in diffusion bridges for distribution transport problems have heavily relied on matching frameworks, yet existing methods often face a trade-off between scalability and access to optimal pairings during training. Fully unsupervised methods make minimal assumptions but incur high computational costs, limiting their practicality. On the other hand, imposing full supervision of the matching process with optimal pairings improves scalability, however, it can be infeasible in many applications. To strike a balance between scalability and minimal supervision, we introduce Feedback Schr""odinger Bridge Matching (FSBM), a novel semi-supervised matching framework that incorporates a small portion (less than 8% of the entire dataset) of pre-aligned pairs as state feedback to guide the transport map of non coupled samples, thereby significantly improving efficiency. This is achieved by formulating a static Entropic Optimal Transport (EOT) problem with an additional term capturing the semi-supervised guidance. The generalized EOT objective is then recast into a dynamic formulation to leverage the scalability of matching frameworks. Extensive experiments demonstrate that FSBM accelerates training and enhances generalization by leveraging coupled pairs guidance, opening new avenues for training matching frameworks with partially aligned datasets.

Problem

• balances scalability and minimal supervision
• improves efficiency with semi-supervised guidance
• accelerates training using coupled pairs guidance

Innovation

• Semi-supervised matching framework
• Feedback Schrödinger Bridge Matching
• Entropic Optimal Transport problem