train with structured dro

This paper addresses distributionally robust optimization (DRO): seeking decisions that remain optimal under the worst-case distribution within an ambiguity set—defined either by Wasserstein distance or φ-divergence—when the true data-generating distribution is unknown. Methodologically, it establishes, for the first time, systematic equivalences between DRO and key machine learning paradigms, including regularization and adversarial training, thereby unifying statistical learning, operations research, and control theory into a coherent theoretical framework. The approach integrates ambiguity set construction, min-max expected loss optimization, duality analysis, and rigorous robustness verification, balancing theoretical interpretability with computational tractability. The resulting methodology significantly enhances model generalization and decision robustness under distributional shifts. It has been successfully deployed in high-stakes domains including financial risk management, medical diagnosis, and AI safety.

This work addresses the limitations of traditional predict-then-optimize approaches, which ignore prediction uncertainty, and existing distributionally robust optimization (DRO) methods that employ fixed-radius ambiguity sets ill-suited for dynamic risk environments. The authors propose a Learnable Prediction Ambiguity Set (LPAS), which jointly learns the center, state-dependent Wasserstein radius, and anisotropic metric of the ambiguity set. This is achieved through end-to-end joint optimization of a deep contextual model and the downstream decision layer, enhanced by conditional quantile calibration and scale regularization to enable state-adaptive robustness. Evaluated on S&P 500 portfolio optimization from 2018 to 2026, LPAS achieves an annualized return of 26.28%, a Sharpe ratio of 1.30, a terminal wealth of 1.61, lower tail risk, and a smaller average ambiguity set radius compared to benchmarks.

Distributionally robust optimization (DRO) faces a fundamental trade-off in ambiguity set design: ensuring fidelity to the nominal distribution while accommodating scenario diversity and preserving computational tractability. Method: We propose diffusion-driven DRO (D-DRO), the first framework to integrate diffusion models into ambiguity set construction. By parameterizing the diffusion process, D-DRO generates a rich, structurally expressive family of adversarial distributions with flexible support—overcoming expressivity limitations inherent in conventional moment- or φ-divergence-based ambiguity sets. Contribution/Results: We establish theoretical guarantees on the stationary convergence of D-DRO solutions. Empirically, D-DRO consistently improves out-of-distribution generalization across diverse machine learning prediction tasks—including regression, classification, and time-series forecasting—while retaining computational efficiency and scalability. The framework bridges statistical robustness, generative modeling, and optimization, offering a principled, expressive, and tractable approach to distributional uncertainty quantification.

To address three key challenges in federated distributionally robust optimization (FDRO) for non-convex settings—difficulty in achieving convergence under asynchronous updates, insufficient exploitation of prior distributional knowledge, and lack of adaptive control over robustness levels—this paper proposes ASPIRE-EASE. The algorithm integrates asynchronous single-loop optimization, alternating gradient projection, and the iterative active-set method (EASE), coupled with a constraint-based D-norm uncertainty set. ASPIRE-EASE establishes the first theoretical convergence guarantee for non-convex FDRO and enables tunable trade-offs between robustness and model performance. Extensive experiments on real-world datasets demonstrate its rapid convergence, strong robustness against data heterogeneity and adversarial attacks, and superior generalization across diverse federated learning scenarios.

This paper studies penalty-based distributionally robust optimization (DRO) with a closed convex uncertainty set, encompassing canonical settings such as $f$-DRO and spectral/$L$-risk minimization. Exploiting the problem’s strongly convex–strongly concave structure, we propose a cyclic–stochastic hybrid sampling scheme, coupled with regularized primal updates and dual variance reduction. This yields the first linearly convergent algorithm whose convergence rate depends *finely* on both primal and dual condition numbers. Theoretical analysis establishes that our method achieves the current state-of-the-art linear convergence rate. Numerical experiments on regression and classification tasks demonstrate significant improvements over existing baseline methods. Our core contributions lie in the synergistic integration of hybrid sampling design, variance reduction, and condition-number-sensitive analysis—establishing a new paradigm for high-accuracy, high-efficiency DRO optimization.

This work addresses the degraded generalization performance of learning-based reconstruction methods under noise or distribution shifts at test time by proposing a structured Distributionally Robust Optimization (DRO) framework. The approach constrains the Wasserstein ambiguity set over the conditional distribution \(P(Y|X)\), enabling precise modeling of uncertainties in the forward operator and noise. Leveraging strong duality theory, the method derives a worst-case risk bound that naturally induces Tikhonov regularization on the Lipschitz constant of the reconstruction operator. Evaluated on image deblurring and CT reconstruction tasks, the proposed framework demonstrates markedly improved robustness, stability, and interpretability compared to standard DRO and MSE baselines. In linear settings, it automatically yields low-rank truncation, effectively reproducing the behavior of data-driven truncated SVD.

This work addresses the lack of finite-sample theoretical guarantees and systematic comparisons for existing robust learning methods under distribution shift between training and deployment environments. Focusing on Distributionally Robust Optimization (DRO) and Robust Satisficing (RS), the paper establishes, for the first time, dimension-free finite-sample generalization error bounds for the target domain and introduces an information-guided hyperparameter calibration strategy that leverages partial knowledge of the distributional shift. Theoretical analysis reveals a complementary relationship between DRO and RS under partial shift information, while empirical studies in inventory network planning demonstrate their distinct response mechanisms to positively shifted demand, thereby providing principled guidance for method selection in practice.

This work investigates the finite-sample statistical performance of distributionally robust optimization (DRO) based on optimal transport (OT) and its regularized variants via f-divergences, with a focus on applications in adversarial training. By establishing concentration inequalities applicable to general OT cost functions, the study provides the first non-asymptotic guarantees for DRO under soft-constrained norm-ball OT neighborhoods. In the p-Wasserstein setting, it achieves improved dependence on the neighborhood size compared to prior results. The proposed approach integrates adversarial example generation with an adversarial reweighting mechanism, thereby not only extending the theoretical foundations of OT-DRO but also enhancing model robustness and empirical performance against adversarial perturbations.