A distributionally robust framework based on optimal transport (OT) for harnessing such heterogeneous data in conditional optimization and demonstrating the value of the framework through a conditional assortment problem using demand and product-feature data from multiple stores is demonstrated.
Abstract
Conditional optimization tailors decisions to contextual or event information, but its practical use is often limited by the difficulty of learning the relevant conditional distribution from finite samples of a target joint distribution. This challenge is especially acute when target joint data are scarce or unavailable, or when few observations fall in the conditioning region of interest. Related joint data may be available from multiple sources, such as different stores, markets, populations, or operating environments, but these sources may be biased relative to the target distribution and cannot be pooled naively. We develop a distributionally robust framework based on optimal transport (OT) for harnessing such heterogeneous data in conditional optimization. The framework constructs ambiguity sets over joint distributions using OT distances to empirical source distributions and optimizes worst-case conditional performance over plausible target laws. We propose three OT ambiguity sets that capture different ways of using heterogeneous sources: enforcing simultaneous source consistency, aggregating source discrepancies through weights, and centering the ambiguity set at an OT barycenter. We derive tractable reformulations, establish feasibility conditions, discuss parameter choices, and characterize the relationships among the formulations, revealing trade-offs between robustness, information aggregation, and computational complexity. We demonstrate the value of the framework through a conditional assortment problem using demand and product-feature data from multiple stores.
A more flexible framework in which a predictive model determines the nominal distribution and a separate model estimates a data-dependent radius is developed, which treats calibration as a practical mechanism for reliable decision making rather than a universal guarantee of improved optimization performance.
The conditional randomization test (CRT) provides a principled approach to conditional independence (CI) testing, guaranteeing exact type-I error control when the true conditional distribution is known. In practice, however, this distribution must be estimated, and estimation errors can inflate type-I errors, while high dimensionality and limited sample sizes can reduce power. Although external and unlabeled data offer the potential to improve CI testing, naive integration that ignores distributional heterogeneity can compromise type-I error control and fail to enhance power. We propose \textbf{CRT*}, a novel framework that robustly integrates external and unlabeled datasets to enhance CI testing in heterogeneous scenarios. CRT* employs smooth residual-bootstrap (SRB) with transfer learning for conditional distribution estimation, combined with adaptive data fusion via an optimal convex combination of test statistics. We theoretically establish that the SRB-based estimator converges to the true conditional distribution in expected total variation distance. Furthermore, even in high-dimensional regimes, CRT* maintains valid type-I error control and achieves strictly higher power than standard CRT without external data. Simulations and RNA-seq breast cancer data analyses demonstrate that CRT* substantially improves power while maintaining type-I error control in heterogeneous settings.
As a popular optimization scheme, distributionally robust optimization (DRO) protects decisions against ambiguity in probability distributions. For (single-stage) DRO, prevailing dual reformulations can become difficult when model or ambiguity-set structures are complex. We study DRO from a primal perspective, working directly with distributions in ambiguity sets on closed, potentially unbounded sample spaces. This perspective leads to an algorithmic framework, referred to as BiCS, that constructs and leverages distribution cuts to achieve strong performance. We show that BiCS is applicable to standard DRO, almost-sure DRO, DRO with various chance constraints, and DRO with ambiguity sets strengthened by local information. Numerical experiments with moment and Wasserstein ambiguity sets show that this framework demonstrates superior performance, including solving cases where the examined compact reformulations are unavailable or computationally difficult. The local-information study also makes changes in worst-case distributions directly visible.
Causal Structure-guided DRO (CS-DRO) is proposed, which estimates a directed acyclic graph (DAG) that encodes the predictive relationships between representations and labels, serving as a proxy for causal structure shared across source domains.
Seonggyeom Kim, Eunjung Choi, Dong-Kyu Chae· Proceedings of the 32nd ACM...· 0 citations
Generative models are increasingly adopted in distributionally robust optimization (DRO), but existing approaches trade off model compatibility and adversarial structure: methods that accept arbitrary samplers do not restrict worst-case laws to a generator family, while generator-parameterized adversaries rely on model-specific access such as likelihoods, scores, or training data. We propose Generative Distributionally Robust Optimization (GDRO), a principled framework that accepts any sampleable conditional generator as the nominal model and restricts worst-case laws to a chosen conditional generator family. The key is the sampler-Sinkhorn pairing: samplers represent the conditional laws exactly, while Sinkhorn divergence compares their induced distributions without likelihood access and can be estimated from samples alone. The resulting population problem admits a direct finite-sample approximation and differentiable primal-dual implementation at the active decision context. For Lipschitz losses, the population Sinkhorn radius bounds downstream degradation. Across explicit and implicit generators, our method reduces rare-context inventory regret by 60% and SocialGAN navigation collisions by 50% relative to nominal decisions.
Ziwei Zhang, Jonathan Yu-Meng Li, Zhihao Jin· arXiv.org· 0 citations
A decision-aware weak-to-strong (W2S) framework that leverages both labeled and unlabeled data to improve contextual stochastic optimization and establishes a non-asymptotic upper bound on the excess decision risk of W2S and a complementary lower bound for a strong-only benchmark.
Jingwei Ji, Renyuan Xu· arXiv.org· 0 citations
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