entropic optimal transport assignments

To address the trade-off between bias and convergence rate induced by entropy regularization in semi-discrete optimal transport (OT), this paper proposes the Dynamic Regularization Annealing Gradient (DRAG) algorithm. DRAG operates within a stochastic gradient descent framework, adaptively decaying the entropy regularization strength while incorporating gradient averaging to progressively eliminate regularization bias without sacrificing computational efficiency. Theoretically, DRAG guarantees $O(1/t)$ convergence rates for both the OT cost and dual potential estimates, and $O(1/sqrt{t})$ convergence for the OT map; moreover, as the regularization coefficient vanishes, the solution converges to the unbiased primal OT solution. Empirical evaluations demonstrate DRAG’s superior accuracy, faster convergence, and enhanced robustness compared to existing methods.

This paper addresses the entropy-regularized optimal transport (EOT) problem by proposing a novel optimization-based framework that dispenses with traditional strong structural assumptions—such as strict convexity or smoothness—required by existing algorithms. Methodologically, it (1) formulates either a semi-dual problem or a nonconvex constrained optimization over a subset of joint distributions, and (2) integrates mirror descent with momentum acceleration to achieve provably accelerated non-asymptotic convergence—attaining a rate of $O(1/k^2)$ under minimal assumptions, matching the acceleration performance of classical Euclidean methods. Theoretically, this work provides the first acceleration guarantee for EOT without requiring strong convexity or smoothness. Furthermore, the framework extends naturally to generalized transport problems, including dynamical Schrödinger bridges, demonstrating both broad applicability and empirical effectiveness.

For large-scale optimal transport (OT) problems, the entropy-regularized Sinkhorn algorithm suffers from numerical instability and slow convergence when the regularization parameter is small. To address this, we propose the Sparse Newton–Proximal Sinkhorn (SNPS) algorithm—a novel coupling of sparse Newton optimization with proximal Sinkhorn iterations. This is the first method to deeply integrate sparse Newton methods into the Sinkhorn framework while preserving global convergence guarantees. Theoretically, we establish rigorous convergence properties; empirically, SNPS achieves near-exact OT solutions on multiple standard benchmarks, with significantly accelerated per-iteration performance. It substantially reduces computational complexity and markedly alleviates sensitivity to the regularization parameter. Compared to state-of-the-art OT solvers, SNPS delivers superior overall performance—achieving high accuracy, high efficiency, and strong robustness simultaneously.

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 cost and curse-of-dimensionality challenges in sampling optimal transport (OT) couplings for large-scale, high-dimensional data, this paper proposes an efficient learning framework based on score-based generative models. Specifically, conditioned on source samples, it iteratively generates target samples following the Sinkhorn-regularized OT coupling via Langevin dynamics. Crucially, it jointly parameterizes the score function and Sinkhorn potential functions—enabling, for the first time, end-to-end co-learning of score-based generation and OT coupling. We theoretically establish the convergence of gradient descent on the network parameters under mild assumptions. Experiments demonstrate that our method significantly improves both accuracy and speed of coupling estimation across diverse large-scale OT tasks, while maintaining scalability and practical applicability.

本文提出SinkSLOT方法，通过稀疏提升的运输计划解决大规模数据集上熵最优传输计算效率低和独立耦合问题。

This study addresses the challenge of non-unique identification of model parameters arising from data insufficiency. To overcome this, it proposes a multi-marginal entropy optimal transport framework that reformulates the partial identification problem as an optimal transport problem over path space, and employs the Sinkhorn iterative algorithm to efficiently solve the resulting infinite-dimensional optimization problem. Theoretically, the paper establishes the convergence of the proposed algorithm and derives the consistency rate of the estimator. Empirically, it demonstrates computationally efficient implementation with precise bound estimation, successfully applying the approach to demand model analysis. Ultimately, this work provides a unified theoretical and computational paradigm for addressing partial identification problems in settings characterized by limited data availability.

This work addresses the lack of a unified theoretical foundation for parameter identifiability, estimation consistency, and algorithmic convergence in feature-parameterized inverse optimal transport (IOT). It proposes an analytical framework based on Sinkhorn linearization and spectral surrogates, which—through the introduction of spectral sandwich inequalities, restricted Hessian analysis, and ℓ₁ regularization—establishes, for the first time, four core theoretical guarantees for IOT: global parameter identifiability, exact support recovery, a Lipschitz continuous inverse mapping, and monotonic convergence of gradient descent. The framework combines geometric transparency with spectral precision and further quantifies the Hölder stability of the projection map under model misspecification. Numerical experiments corroborate the theoretical findings.

This work addresses the computational challenges of large-scale entropy-regularized optimal transport, which is notoriously difficult to solve efficiently due to its high complexity. Existing GPU-based methods struggle to balance convergence speed and parallel efficiency. To overcome this limitation, we propose a high-performance GPU solver that synergistically combines the strengths of quasi-Newton methods and the Sinkhorn algorithm. Our approach introduces several key innovations: amortized sign analysis, asynchronous Sinkhorn iterations, and fused gradient kernels, complemented by sparse-plus-low-rank approximations, asynchronous computation, and optimized memory access patterns. While preserving theoretical convergence guarantees, the proposed method consistently outperforms state-of-the-art GPU solvers across multiple benchmark tasks, achieving substantial acceleration.

This work addresses the rigidity of classical optimal transport in scenarios where mass conservation does not hold and its poor sample complexity in high dimensions. The authors investigate the finite-sample theory of entropy-regularized unbalanced optimal transport, introducing a translation-invariant dual formulation and analyzing its geometric structure. They establish, for the first time, high-probability convergence bounds for empirical optimal couplings at the coupling level. Their analysis demonstrates that entropy regularization not only substantially mitigates the curse of dimensionality and reduces the required sample size but also enhances estimation stability, all while preserving compatibility with efficient solvers such as Sinkhorn algorithms.