Jonathan Yu-Meng Li

Qinyu Wu, Jonathan Yu-Meng Li, Tiantian Mao

Wasserstein distributionally robust optimization (DRO) has gained prominence in operations research and machine learning as a powerful method for achieving solutions with favorable out-of-sample performance. Two compelling explanations for its success are the generalization bounds derived from Wasserstein DRO and its equivalence to regularization schemes commonly used in machine learning. However, existing results on generalization bounds and regularization equivalence are largely limited to settings where the Wasserstein ball is of a specific type, and the decision criterion takes certain forms of expected functions. In this paper, we show that generalization bounds and regularization equivalence can be obtained in a significantly broader setting, where the Wasserstein ball is of a general type and the decision criterion accommodates any form, including general risk measures. This not only addresses important machine learning and operations management applications but also expands to general decision-theoretical frameworks previously unaddressed by Wasserstein DRO. Our results are strong in that the generalization bounds do not suffer from the curse of dimensionality and the equivalency to regularization is exact. As a by-product, we show that Wasserstein DRO coincides with the recent max-sliced Wasserstein DRO for {\it any} decision criterion under affine decision rules -- resulting in both being efficiently solvable as convex programs via our general regularization results. These general assurances provide a strong foundation for expanding the application of Wasserstein DRO across diverse domains of data-driven decision problems.

Nima Afsharhajari, Jonathan Yu-Meng Li

Sparsity or complexity? In modern high-dimensional asset pricing, these are often viewed as competing principles: richer feature spaces appear to favor complexity, while economic intuition has long favored parsimony. We show that this tension is misplaced. We distinguish capacity sparsity-the dimensionality of the candidate feature space-from factor sparsity-the parsimonious structure of priced risks-and argue that the two are complements: expanding capacity enables the discovery of factor sparsity. Revisiting the benchmark empirical design of Didisheim et al. (2025) and pushing it to higher complexity regimes, we show that nonlinear feature expansions combined with basis pursuit yield portfolios whose out-of-sample performance dominates ridgeless benchmarks beyond a critical complexity threshold. The evidence shows that the gains from complexity arise not from retaining more factors, but from enlarging the space from which a sparse structure of priced risks can be identified. The virtue of complexity in asset pricing operates through factor sparsity.

Ziwei Zhang, Jonathan Yu-Meng Li

Modern stochastic optimization pipelines increasingly rely on learned generative models to represent uncertainty, while downstream decisions are evaluated almost entirely through Monte Carlo scenarios. This shifts the operational object of uncertainty from an explicit probability law to the sampler induced by the learned generator. Reliability therefore depends on two errors: sampler misspecification and finite-simulation error. We propose Sampler-Robust Optimization (SRO), which optimizes decisions against the worst-case sampler induced by perturbing the learned generator. This sampler-first formulation aligns with simulation-based decision pipelines and admits a sharpness-aware interpretation: it favors decisions whose performance is stable under generator perturbations, rather than merely under the nominal sampler. Under a coverage assumption, we show that the empirical worst-case objective provides a high-probability upper certificate for the true population objective, with finite-simulation error partially absorbed by the robustification used to guard against sampler misspecification. The framework accommodates generative models with or without explicit densities and admits efficient minimax procedures. Portfolio-optimization experiments show that SRO produces more stable decisions and improves out-of-sample performance under distribution shift.

Xinqiao Xie, Jonathan Yu-Meng Li

Conditional risk minimization arises in high-stakes decisions where risk must be assessed in light of side information, such as stressed economic conditions, specific customer profiles, or other contextual covariates. Constructing reliable conditional distributions from limited data is notoriously difficult, motivating a series of optimal-transport-based proposals that address this uncertainty in a distributionally robust manner. Yet these approaches remain fragmented, each constrained by its own limitations: some rely on point estimates or restrictive structural assumptions, others apply only to narrow classes of risk measures, and their structural connections are unclear. We introduce a universal framework for distributionally robust conditional risk minimization, built on a novel union-ball formulation in optimal transport. This framework offers three key advantages: interpretability, by subsuming existing methods as special cases and revealing their deep structural links; tractability, by yielding convex reformulations for virtually all major risk functionals studied in the literature; and scalability, by supporting cutting-plane algorithms for large-scale conditional risk problems. Applications to portfolio optimization with rank-dependent expected utility highlight the practical effectiveness of the framework, with conditional models converging to optimal solutions where unconditional ones clearly do not.