Distributionally robust optimization (DRO) minimizes worst-case risk under distributional uncertainty, but its decisions can be suboptimal in terms of their excess risk, or regret. We study this gap for multivariate least-squares regression, assuming that the observed source law and unknown target law differ by an adversarial 2-Wasserstein perturbation of size \(\varepsilon\). We first identify the … Read more
We study robust network enhancement problems that improve network performance through component upgrades, where both network utilities and enhancement costs are uncertain. We consider two formulations: a lower-bound problem that improves the minimum utility across feasible network structures and an upper-bound problem that improves the maximum utility. For the lower-bound problem, we develop an exact … Read more
We propose robust and distributionally robust formulations of the risk budgeting problem under the mean absolute deviation (MAD) risk measure. The proposed models address uncertainty in asset returns and their distribution while allocating portfolio risk according to prescribed risk budgets. We first develop a robust model in which historical return observations are perturbed within a … Read more
Distributionally robust optimization hedges a decision against an ambiguity set of candidate distributions. In a cold-start setting the target distribution is unobserved and no sample from it is available, so only related source distributions provide evidence for constructing that set. We propose an inclusive-exclusive Wasserstein ball model that jointly learns a center and radius from … Read more
We study robust optimization problems with decision-dependent information discovery under polyhedral uncertainty and continuous recourse. We first establish structural properties of the resulting min–max–min problem, including existence of solutions and a condition under which information discovery has no value. Then, we develop a heuristic approach that combines affine decision rules with scenario generation and show … Read more
Deep hedging learns trading policies from historical or simulated market trajectories, yet under nonstationarity these training paths may not represent future market conditions. We propose WRAP (Wasserstein-Reweighting Adversarial Perturbation), a drift-aware adversarial training framework derived from a two-budget distributionally robust optimization (DRO) formulation. The formulation is anchored to a weighted empirical reference distribution whose fixed … Read more
We study stochastic optimization with a completely unobserved target distribution and samples from related source distributions. Treating the sources and the target as independent draws from a common meta-distribution, we propose Wasserstein-metric meta-distribution support learning (MDSL). The model jointly learns the center and radius of a Wasserstein ball, with an exclusion parameter controlling the fraction … Read more
We study the well-posedness and convergence of column-and-constraint generation algorithms for general two-stage robust optimization problems. The analysis is formulated in terms of regularity properties of the objective, the second-stage feasible region mapping, and the separation value function, without relying on a particular algebraic representation of the second-stage problem. We give sufficient conditions for the … Read more
Classical budget uncertainty is widely used in robust optimization. It bounds the aggregate absolute deviation of uncertain parameters from nominal values and yields tractable robust counterparts. In many applications, however, information concerns aggregate signed deviations. We therefore study signed budget uncertainty, in which bounds are imposed on signed aggregates rather than absolute deviations. For robust … Read more
Distributionally robust optimization (DRO) provides a principled framework for learning under distribution shift, but its practical use is hindered by the difficulty of evaluating worst-case risks for nonconvex loss functions. We study a penalized DRO formulation in which the adversary may choose any distribution but incurs a Wasserstein penalty for deviating from the empirical distribution. … Read more