Drift-admissibility via Optimal Transport
Abstract
We introduce structure-aware optimal transport diagnostics for assessing whether empirical time-series dynamics are compatible with a prescribed predictable-drift class. Our approach translates a pathwise property of stochastic processes into a finite-dimensional projection problem over empirical transition laws, encoding admissibility as row-wise moment constraints on local couplings and quantifying deviations via a Kullback--Leibler projection gap Gλ,k. This yields both a principled diagnostic and a scalable Bregman--Dykstra algorithm that retains the efficiency of Sinkhorn-type methods while incorporating structural constraints. Calibrated against a Brownian reference null, Gλ,k separates process classes that are indistinguishable by second-order statistics alone---including fractional Brownian motion and BSS processes sharing identical Hurst indices---without asymptotic resampling or continuous-time recovery. This positions the method as a general tool for structure-aware model validation of sequential data.
Related
- Ornstein-Uhlenbeck Is Hard to Beat, Yet Superlinear Drift Ships Lower Transport Costs
- Regret-Optimal Linear-Quadratic Control under Distributional Drift
- Beyond Aggregate Drift: Optimal Client-Specific Windows in Federated Learning
- Prior-Shift-Invariant Threshold Transport in Budget-Constrained Supervisory Screening: Workload Identity, Prior–Drift Decomposition, and Distribution-Free Risk Control
- Sparsity of Quadratically Regularized Optimal Transport: Scalar Case
BibTeX
@misc{langbridge2026driftadmissibility,
title = {{Drift-admissibility via Optimal Transport}},
author = {Abigail Langbridge and Enrico Biffis and Jakub Mareček and Robert Shorten},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08505},
eprint = {2611.08505},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08505},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Drift-admissibility via Optimal Transport
AU - Abigail Langbridge
AU - Enrico Biffis
AU - Jakub Mareček
AU - Robert Shorten
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.08505
UR - https://arxiv.org/abs/2611.08505
AB - We introduce structure-aware optimal transport diagnostics for assessing whether empirical time-series dynamics are compatible with a prescribed predictable-drift class. Our approach translates a pathwise property of stochastic processes into a finite-dimensional projection problem over empirical transition laws, encoding admissibility as row-wise moment constraints on local couplings and quantifying deviations via a Kullback--Leibler projection gap G_λ,k. This yields both a principled diagnostic and a scalable Bregman--Dykstra algorithm that retains the efficiency of Sinkhorn-type methods while incorporating structural constraints. Calibrated against a Brownian reference null, G_λ,k separates process classes that are indistinguishable by second-order statistics alone---including fractional Brownian motion and BSS processes sharing identical Hurst indices---without asymptotic resampling or continuous-time recovery. This positions the method as a general tool for structure-aware model validation of sequential data.
ER -