arXiv AI October 2, 2026 By Jinhwan Sul, Panagiotis Theodoropoulos, Vincent Pacelli, Jaemoo Choi, Evangelos Theodorou

Distributionally Robust Schr\"odinger Bridge

The paper introduces the Distributionally Robust Schr"odinger Bridge (DRSB), a method that learns a single controller capable of handling uncertainty in the initial distribution for stochastic transport tasks. DRSB’s objective combines control energy with a KL penalty on the terminal distribution, and it seeks to minimize the worst‑case value of this objective over an ambiguity set around the nominal initial distribution. The authors derive a variational formulation, connect it to stochastic optimal control and distributionally robust optimization, and propose an alternating algorithm with Wasserstein and Sinkhorn variants. Experiments on two‑dimensional transport and image‑to‑image translation demonstrate improved robustness to input perturbations compared to standard SB, while also achieving lower mean sliced Wasserstein distance on Gaussian mixture transport.

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safety

arXiv Statistics ML

6d ago

Brenier Meets Adversarial Training: Optimal Transport Geometry for Robust Learning

The paper introduces a penalized distributionally robust optimization framework that allows an adversary to choose any distribution while incurring a Wasserstein penalty for deviating from the empirical distribution. It shows that the adversary’s problem can be reformulated as optimizing transport maps that push empirical samples to adversarial ones, proving that optimal maps are cyclically monotone. The authors argue that standard per-sample adversarial training violates this property and propose two remedies—multi-start particle ascent and input-convex neural network parameterization—to enforce cyclical monotonicity, demonstrating improved robustness and generalization in experiments on regression, image classification, and control tasks.

By Alireza Abdollahpoorrostam, Ehsan Sharifian, Buse \c{S}en, Marco Cuturi, Daniel Kuhn

computer-vision benchmarks safety

arXiv Machine Learning

Sep 1

Data-to-Energy Stochastic Dynamics

arXiv:2509.26364v3 Announce Type: replace Abstract: The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certa...

By Kirill Tamogashev, Esmeralda S. Whitammer

diffusion reinforcement-learning multimodal

arXiv Machine Learning

Jul 10

Wasserstein Distributionally Robust Regret Optimization for Reinforcement Learning from Human Feedback

arXiv:2605. 00155v3 Announce Type: replace Abstract: Reinforcement learning from human feedback (RLHF) is a central post-training tool for aligning large language models, but its training reward is only a learned proxy for true human utility.

By Yikai Wang, Shang Liu, Jose Blanchet

llms reinforcement-learning

arXiv Machine Learning

Jul 17

Distributionally Robust Optimization via Iterative Algorithms in Continuous Probability Spaces

arXiv:2412. 20556v2 Announce Type: replace-cross Abstract: We study distributionally robust optimization (DRO) for robust inference when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem.

By Linglingzhi Zhu, Yunqin Zhu, Yao Xie

arXiv Machine Learning

Jul 14

Distributionally Robust Reinforcement Learning with Interactive Data Collection: Fundamental Hardness and Near-Optimal Algorithms

arXiv:2404. 03578v3 Announce Type: replace Abstract: The sim-to-real gap, which represents the disparity between training and testing environments, poses a significant challenge in reinforcement learning (RL).

By Miao Lu, Han Zhong, Tong Zhang, Jose Blanchet

reinforcement-learning robotics

arXiv Machine Learning

Jul 21

Representation-Aware Distributionally Robust Optimization: A Knowledge Transfer Framework

arXiv:2509. 09371v2 Announce Type: replace-cross Abstract: Distributionally robust optimization (DRO) protects statistical learning against distributional shifts by optimizing the worst-case performance over a set of perturbed distributions.

By Zitao Wang, Nian Si, Molei Liu

fine-tuning

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