arXiv Statistics ML
Sep 28

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
arXiv AI
Oct 2

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.

By Jinhwan Sul, Panagiotis Theodoropoulos, Vincent Pacelli, Jaemoo Choi, Evangelos Theodorou
arXiv Machine Learning
Sep 22

Robust Market Making with Hawkes Order Flow and Price Impact via Adversarial Reinforcement Learning

The paper proposes an adversarial reinforcement‑learning framework for market making that incorporates Hawkes‑process driven order arrivals and trade‑induced price impact, addressing limitations of prior Poisson‑based models. An LSTM module captures temporal dependencies in recent observations to handle increased non‑stationarity, and the authors analyze equilibrium properties and introduce a robustness evaluation protocol focused on the left tail of returns. Experiments across diverse market regimes demonstrate that the method improves left‑tail performance, especially under strong Hawkes excitation and moderate price impact, without relying on a terminal inventory bias.

By Hao Yang, Zhenguo Xu