Distributionally Robust Optimization (DRO) offers a promising framework by optimizing worst-case performance over a set of candidate distributions, referred to as the uncertainty set. However, the efficacy of DRO heavily depends on the design of the uncertainty set, and existing methods often perform suboptimally due to an inappropriate or inflexible uncertainty set. In this work, we first propose a novel perspective that casts entropy-regularized Wasserstein DRO as a dynamic process of distributional exploration and semantic alignment, both driven by optimal transport (OT). This unified viewpoint yields two key new techniques: semantic calibration, which bootstraps semantically meaningful transport costs via inverse OT, and adaptive refinement, which adjusts uncertainty set using OT-driven feedback. Together, these components form an exploration-and-feedback system, where the transport costs and uncertainty set evolve jointly during training, enabling the model to better adapt to potential distribution shifts. Moreover, we provide an in-depth analysis of this adaptive process and prove theoretical guarantees of convergence. Finally, we present our experimental results across diverse distribution shift scenarios, which demonstrate that our approach significantly outperforms existing methods, achieving state-ofthe-art robustness.

Distributionally Robust Optimization (DRO) offers a promising framework by optimizing worst-case performance over a set of candidate distributions, which is called as the \emph{uncertainty set}. However, the efficacy of DRO heavily depends on the design of uncertainty set, and existing methods often perform suboptimally due to inappropriate and inflexible uncertainty sets. In this work, we first propose a novel perspective that casts entropy-regularized Wasserstein DRO as a dynamic process of distributional exploration and semantic alignment, both driven by optimal transport (OT). This unified viewpoint yields two key new techniques: \emph{semantic calibration}, which bootstraps semantically meaningful transport costs via inverse OT, and \emph{adaptive refinement}, which adjusts uncertainty set using OT-driven feedback. Together, these components form an exploration-and-feedback system, where the transport costs and uncertainty set evolve jointly during training, enabling the model to better adapt to potential distribution shifts. Moreover, we provide an in-depth analysis on this adaptive process and prove the theoretical convergence guarantee. Finally, we present our experimental results across diverse distribution shift scenarios, which demonstrate that our approach significantly outperforms existing methods, achieving state-of-the-art robustness.

Medical image harmonization aims to reduce the differences in appearance caused by scanner hardware variations to allow for consistent and reliable comparisons across devices. Harmonization based on paired images from different devices has limited applicability in real-world clinical settings. On the other hand, unpaired harmonization typically does not guarantee anatomy consistency, which is problematic because anatomical information preservation is paramount. The Schrödinger bridge framework has achieved state-of-the-art style transfer performance with natural images by matching distributions of unpaired images, but this approach can also introduce anatomy changes when applied to medical images. We show that such changes occur because the Schrödinger bridge uses the square of the Euclidean distance between images as the transport cost in an entropy-regularized optimal transport problem.

The example shows the learned IT map with high w =2 0 approximating the ET map.

In many unpaired image domain translation problems, e.g., style transfer or super-resolution, it is important to keep the translated image similar to its respective input image.

Neural Information Processing Systems http://nips.cc/

Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two individuals from any two given groups in the OT plan satisfies a predefined target. We first propose \texttt{FairSinkhorn}, a modified Sinkhorn algorithm to compute perfectly fair transport plans efficiently. Since exact fairness can significantly degrade matching quality in practice, we then develop two relaxation strategies. The first one involves solving a penalised OT problem, for which we derive novel finite-sample complexity guarantees. This result is of independent interest as it can be generalized to arbitrary convex penalties. Our second strategy leverages bilevel optimization to learn a ground cost that induces a fair OT solution, and we establish a bound guaranteeing that the learned cost yields fair matchings on unseen data. Finally, we present empirical results that illustrate the trade-offs between fairness and performance.

Topological data analysis (TDA) has been used successfully in a wide array of applications, for instance in medical (Nicolau et al., 2011) or material (Hiraoka et al., 2016) sciences, computer vision (Li et al., 2014) or to classify NBA players (Lum et al., 2013).

Optimal transport (OT) has emerged as a fundamental computational tool across many areas, including machine learning, computer vision, statistics, and biology [Arjovsky et al., 2017, Peyr e and Cuturi, 2019, Schiebinger et al., 2019, Bonneel and Digne, 2023]. It provides a principled framework for comparing probability distributions, and it has a rich mathematical history [Villani et al., 2008]. While the combination of practical utility and deep mathematical theory has led to the broad adoption of OT ideas in mathematics, science, and engineering, finding ways to scale OT solutions and make them interpretable remains a fundamental research question [Cuturi et al., 2023, Khamis et al., 2024]. In particular, OT typically suffers from the curse of dimensionality [Chewi et al., 2025], and regularized estimators may lack sparsity [Genevay et al., 2019]. A long line of work has focused on making OT scalable and interpretable through regularization. The most classical of these is entropic regularization, which yields a strictly convex program that can be solved via Sinkhorn scaling [Sinkhorn, 1967, Cuturi, 2013]. More recent work has sought to increase efficiency and interpretability through quadratic regularization [Blondel et al., 2018, Lorenz et al., 2021], as well as low-rank factorizations [Forrow et al., 2019, Scetbon et al., 2021]. These methods show promise in biological applications, particularly in single-cell RNA sequencing analysis [Klein et al., 2025]. Another closely related set of recent works attempts to include sparsity in the OT map using elastic costs Cuturi et al. [2023], Klein et al. [2024], Chen et al. [2025].

The example shows the learned IT map with high w =2 0 approximating the ET map.