Related papers: Scenario-based Regularization: A Tractable Framewo…
Stochastic and (distributionally) robust optimization problems often become computationally challenging as the number of scenarios or data points increases. Scenario reduction is therefore a key technique for improving tractability. We…
In data-driven optimization, sample average approximation (SAA) is known to suffer from the so-called optimizer's curse that causes an over-optimistic evaluation of the solution performance. We argue that a special type of distributionallly…
Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein…
Regularized estimators in the context of group variables have been applied successfully in model and feature selection in order to preserve interpretability. We formulate a Distributionally Robust Optimization (DRO) problem which recovers…
Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees,…
Decision-makers often encounter uncertainty, and the distribution of uncertain parameters plays a crucial role in making reliable decisions. However, complete information is rarely available. The sample average approximation (SAA) approach…
Scenario reduction (SR) alleviates the computational complexity of scenario-based stochastic optimization with conditional value-at-risk (SBSO-CVaR) by identifying representative scenarios to depict the underlying uncertainty and tail…
In recent years, Wasserstein Distributionally Robust Optimization (DRO) has garnered substantial interest for its efficacy in data-driven decision-making under distributional uncertainty. However, limited research has explored the…
Applications such as adversarially robust training and Wasserstein Distributionally Robust Optimization (WDRO) can be naturally formulated as min-sum-max optimization problems. While this formulation can be rewritten as an equivalent…
This paper concerns a high-dimensional stochastic programming problem of minimizing a function of expected cost with a matrix argument. To this problem, one of the most widely applied solution paradigms is the sample average approximation…
This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…
Despite superior performance in many situations, deep neural networks are often vulnerable to adversarial examples and distribution shifts, limiting model generalization ability in real-world applications. To alleviate these problems,…
We investigate a stochastic program with expected value constraints, addressing the problem in a general context through Distributionally Robust Optimization (DRO) approach using Wasserstein distances, where the ambiguity set depends on the…
Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not…
A large class of stochastic programs involve optimizing an expectation taken with respect to an underlying distribution that is unknown in practice. One popular approach to addressing the distributional uncertainty, known as the…
We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the covariates is reduced to a finite data sample of their joint…
We study a variety of Wasserstein distributionally robust optimization (WDRO) problems where the distributions in the ambiguity set are chosen by constraining their Wasserstein discrepancies to the empirical distribution. Using the notion…
Wasserstein distributionally robust optimization (WDRO) optimizes against worst-case distributional shifts within a specified uncertainty set, leading to enhanced generalization on unseen adversarial examples, compared to standard…
We consider the distributionally robust optimization (DRO) problem with spectral risk-based uncertainty set and $f$-divergence penalty. This formulation includes common risk-sensitive learning objectives such as regularized condition…
We propose a Distributionally Robust Optimization (DRO) formulation with a Wasserstein-based uncertainty set for selecting grouped variables under perturbations on the data for both linear regression and classification problems. The…