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This research introduces Causal Sinkhorn DRO (Causal-SDRO), a novel framework that integrates causal consistency with continuous distributional robustness to enhance decision-making under uncertainty. By combining an entropy-regularized causal Wasserstein distance with a differentiable soft regression forest, the method offers a tractable, interpretable solution for worst-case scenarios in complex environments. The approach advances the intersection of causal inference and optimization, providing a rigorous mathematical foundation for building more robust AI systems.
Contextual Distributionally Robust Optimization with Causal and Continuous Structure
arXiv:2601.11016v3 Announce Type: replace-cross Abstract: We propose a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution, and we develop an interpretable and tractable decision rule. We first introduce the causal Sinkhorn discrepancy (CSD), an entropy-regularized causal Wasserstein distance that encourages continuous transport plans while preserving 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 obtain an (infinite-dimensional) optimal policy, we propose a soft regression forest (SRF) decision rule: it preserves the interpretability of classical decision trees while being fully parametric, differentiable, and Lipschitz-smooth, enabling intrinsic interpretation from both global and local perspectives. To solve the Causal-SDRO with parametric decision rules, we develop an efficient stochastic compositional gradient algorithm that converges to an $\varepsilon$-stationary point at a rate of $\mathcal{O}(\varepsilon^{-4})$, matching that of standard stochastic gradient descent. Finally, we validate our method through numerical experiments on synthetic and real-world datasets, demonstrating its superior performance and interpretability.
Abstract:We propose a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution, and we develop an interpretable and tractable decision rule. We first introduce the causal Sinkhorn discrepancy (CSD), an entropy-regularized causal Wasserstein distance that encourages continuous transport plans while preserving 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 obtain an (infinite-dimensional) optimal policy, we propose a soft regression forest (SRF) decision rule: it preserves the interpretability of classical decision trees while being fully parametric, differentiable, and Lipschitz-smooth, enabling intrinsic interpretation from both global and local perspectives. To solve the Causal-SDRO with parametric decision rules, we develop an efficient stochastic compositional gradient algorithm that converges to an $\varepsilon$-stationary point at a rate of $\mathcal{O}(\varepsilon^{-4})$, matching that of standard stochastic gradient descent. Finally, we validate our method through numerical experiments on synthetic and real-world datasets, demonstrating its superior performance and interpretability.
Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Optimization and Control (math.OC)
arXiv:2601.11016 [stat.ML]
(or arXiv:2601.11016v3 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2601.11016 Focus to learn more arXiv-issued DOI via DataCite
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