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We study first-order optimality conditions for constrained optimization in the Wasserstein space, whereby one seeks to minimize a real-valued function over the space of probability measures endowed with the Wasserstein distance. Our…
In this paper, we propose a practical online method for solving a class of distributionally robust optimization (DRO) with non-convex objectives, which has important applications in machine learning for improving the robustness of neural…
We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show…
Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…
This paper introduces a new modeling framework for optimization under uncertainty, called Probable Event Constrained Optimization (PECO). Unlike conventional chance-constrained formulations, which only limit the probability of constraint…
We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…
We consider a residuals-based distributionally robust optimization (DRO) model, where the underlying uncertainty depends on both covariate information and our decisions. We adopt both parametric and nonparametric regression models to learn…
We propose a data-driven method to establish probabilistic performance guarantees for parametric optimization problems solved via iterative algorithms. Our approach addresses two key challenges: providing convergence guarantees to…
This paper proposes a novel approach to construct data-driven online solutions to optimization problems (P) subject to a class of distributionally uncertain dynamical systems. The introduced framework allows for the simultaneous learning of…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
We consider decision-making problems under decision-dependent uncertainty (DDU), where the distribution of uncertain parameters depends on the decision variables and is only observable through a finite offline dataset. To address this…
This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite…
Noisy data are often viewed as a challenge for decision-making. This paper studies a distributionally robust optimization (DRO) that shows how such noise can be systematically incorporated. Rather than applying DRO to the noisy empirical…
The aim of this paper is to address the challenge of gradual domain adaptation within a class of manifold-constrained data distributions. In particular, we consider a sequence of $T\ge2$ data distributions $P_1,\ldots,P_T$ undergoing a…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
We propose an online data compression approach for efficiently solving distributionally robust optimization (DRO) problems with streaming data while maintaining out-of-sample performance guarantees. Our method dynamically constructs…
Distributionally robust optimization (DRO)-based robust adaptive beamforming (RAB) enables enhanced robustness against model uncertainties, such as steering vector mismatches and interference-plus-noise covariance matrix estimation errors.…
We introduce a robust variant of the Kelly portfolio optimization model, called the Wasserstein-Kelly portfolio optimization. Our model, taking a Wasserstein distributionally robust optimization (DRO) formulation, addresses the fundamental…
The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization…
Wasserstein \textbf{D}istributionally \textbf{R}obust \textbf{O}ptimization (DRO) is concerned with finding decisions that perform well on data that are drawn from the worst-case probability distribution within a Wasserstein ball centered…