interaction-aware optimal transport

This study addresses a critical limitation in existing generative models, where coupling design relies solely on transport cost while neglecting routing discrepancies, leading to evaluation biases between Flow Matching (FM) and Optimal Transport (OT). We propose a decoupled perspective of routing and cost, revealing their fundamental distinctions within FM and OT frameworks. By leveraging exact FM trajectories as an oracle to construct route-aware training couplings, our approach transcends the conventional paradigm of mere cost minimization. Both theoretical analysis and neural network-based empirical evaluations demonstrate that the proposed coupling significantly outperforms cost-equivalent baselines in directional consistency. These findings confirm that jointly optimizing transport cost and routing is essential for enhancing generation quality.

该文综述了最优传输理论在经济学中的应用，通过Kantorovich对偶等方法解决资源配置、均衡及计算问题，并探讨其作为匹配模型和工具的角色。

This paper addresses the Hierarchical Optimal Transport (HOT) problem under multi-source heterogeneous transportation costs—a computationally challenging generalization of standard optimal transport. Method: We propose an efficient solution framework grounded in chordal graph theory: (i) we introduce a novel algebraic characterization of hierarchical transport structure using chordal graphs, enabling reduction of HOT to a standard optimal transport problem; (ii) we design an algebraic composition method for cost matrices to model adversarial multi-choice transportation costs; and (iii) we develop the first polynomial-time algorithm for exact and efficient synthesis of hierarchical transport plans. Results: Experiments demonstrate that our approach significantly outperforms naive solvers in both computational efficiency and solution quality. It exhibits strong practicality and scalability in large-scale hierarchical transportation settings, offering a theoretically grounded and empirically robust alternative for structured optimal transport.

Networked transportation systems exhibit insufficient robustness under sudden disruptions (e.g., natural disasters). Method: This paper proposes Imitation-regularized Optimal Transport (I-OT), the first framework integrating imitation learning into graph-structured optimal transport. It mathematically embeds human domain knowledge to enhance model interpretability and practicality. Theoretically, I-OT builds upon entropy-regularized optimal transport and convex optimization analysis to rigorously establish transmission stability under node/edge failures and accelerated convergence. Technically, it combines graph neural network-based modeling with simulation-driven validation. Results: Evaluated on automotive parts logistics simulation, I-OT significantly improves path scheduling robustness. Moreover, it establishes an interpretable theoretical linkage between the learned transport policy and real-world logistics resilience—bridging algorithmic design with operational reliability.

To address the high computational complexity and memory bottlenecks in computing Wasserstein distances for large-scale optimal transport, this paper proposes a projection gradient descent framework grounded in orthogonal coupling dynamics. Methodologically, it introduces— for the first time—the conditional expectation as a microscopic evolution mechanism, integrating insights from opinion dynamics to construct a lightweight differential coupling system that enables scalable reconstruction of stochastic transport maps. Unlike conventional infinite-dimensional linear programming approaches, our method breaks polynomial-time and memory-storage barriers, achieving substantial gains in computational efficiency and memory scalability. Experiments demonstrate high-fidelity recovery of transport maps, enabling real-time learning and deployment of both Wasserstein distances and optimal transport plans. This work establishes a novel paradigm for large-scale optimal transport.

本文提出了一种动态广义Gromov-Wasserstein最优传输方法TP-DATE，通过路径作用和流动匹配技术，在保持组织结构的同时改进了连续3D动态重构。

This work addresses the challenge of effectively integrating a small amount of coupled data with abundant uncoupled marginal observations to enhance downstream statistical inference. The authors propose a fully nonparametric approach that aligns marginal data with limited coupled samples via optimal transport projections and introduces an explicit estimator grounded in the notion of “shadow” couplings to extrapolate the dependence structure and improve estimation accuracy. The method offers geometric interpretability, numerical stability, and near-linear-time parallelizability. Theoretical guarantees are established by synthesizing tools from optimal transport theory, projection-based estimation, and sample complexity analysis. Extensive experiments on both synthetic and real-world datasets demonstrate the method’s high accuracy and computational efficiency.

This study addresses the implementability of heterogeneous user edge flows in dynamic networks with either multiple origins and destinations or multiple origins and a single destination—specifically, whether such flows can be induced as dynamic equilibrium flows through suitably designed tolls. To this end, the authors formulate an infinite-dimensional optimization model, leveraging a refined understanding of the underlying network loading structure and extending Zareckiĭ’s Lusin $N^{-1}$ property for absolutely continuous monotone functions to establish novel criteria for the existence of dynamic loadings. The main contributions include a dual characterization for the multi-origin–multi-destination setting, and for the multi-origin–single-destination case, both combinatorial and dual characterizations are obtained, along with a proof that any edge flow with finite support necessarily satisfies the strong duality condition.

This study addresses the failure of traditional divergence measures in reinforcement learning (RL) caused by weakly overlapping state distributions by introducing optimal transport (OT) theory. Through a systematic review of OT's application motivations, objective functions, and algorithmic designs in RL, this work proposes a unified framework that integrates OT theory with reinforcement learning. The primary contributions include establishing a comprehensive taxonomy that incorporates practical considerations, providing an in-depth analysis of the core role of OT in policy optimization, and explicitly identifying open challenges such as scalability and theoretical analysis. Ultimately, this research offers clear guidance for future investigations within this interdisciplinary domain.

该论文提出了一种结合少量标注地标的新耦合最优传输框架，以解决仅通过最小化传输成本无法找到几何上有意义的分布变换的问题。