[2601.11016] Contextual Distributionally Robust Optimization with Causal and Continuous Structure: An Interpretable and Tractable Approach

Statistics > Machine Learning arXiv:2601.11016 (stat) [Submitted on 16 Jan 2026 (v1), last revised 2 Apr 2026 (this version, v2)] Title:Contextual Distributionally Robust Optimization with Causal and Continuous Structure: An Interpretable and Tractable Approach Authors:Fenglin Zhang, Jie Wang View a PDF of the paper titled Contextual Distributionally Robust Optimization with Causal and Continuous Structure: An Interpretable and Tractable Approach, by Fenglin Zhang and Jie Wang View PDF Abstract:In this paper, we introduce a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution by developing interpretable and tractable decision rules that prescribe decisions using covariates. We first introduce the causal Sinkhorn discrepancy (CSD), an entropy-regularized causal Wasserstein distance that encourages continuous transport plans while preserving the causal consistency. We then formulate a contextual DRO model with a CSD-based ambiguity set, termed Causal Sinkhorn DRO (Causal-SDRO), and derive its strong dual reformulation where the worst-case distribution is characterized as a mixture of Gibbs distributions. To solve the corresponding infinite-dimensional policy optimization, we propose the Soft Regression Forest (SRF) decision rule, which approximates optimal policies within arbitrary measurable function spaces. The SRF preserves the interpretability of classical decision trees whil...