Wasserstein Distributionally Robust Optimization with Heterogeneous Data Sources

We study decision problems under uncertainty, where the decision-maker has access to K data sources that carry biased information about the underlying risk factors. The biases are measured by the mismatch between the risk factor distribution and the K data-generating distributions with respect to an optimal transport (OT) distance. In this situation the decision-maker can … Read more

A Decomposition Algorithm for Distributionally Robust Chance-Constrained Programs with Polyhedral Ambiguity Set

In this paper, we study a distributionally robust optimization approach to chance-constrained stochastic programs to hedge against uncertainty in the distributions of the random parameters. We consider a general polyhedral ambiguity set under finite support and study Wasserstein ambiguity set, total variation distance ambiguity set, and moment-based ambiguity set as examples for our computations. We … Read more

Distributionally Robust Optimization with Decision-Dependent Polyhedral Ambiguity

We consider a two-stage stochastic program with continuous recourse, where the distribution of the random parameters depends on the decisions. Assuming a finite sample space, we study a distributionally robust approach to this problem, where the decision-dependent distributional ambiguity is modeled with a polyhedral ambiguity set. We consider cases where the recourse function and the … Read more

Robust Drone Delivery with Weather Information

Problem definition: Drone delivery has recently garnered significant attention due to its potential for faster delivery at a lower cost than other delivery options. When scheduling drones from a depot for delivery to various destinations, the dispatcher must take into account the uncertain wind conditions, which affect the delivery times of drones to their destinations, … Read more

Distributionally Robust Optimization with Decision-Dependent Information Discovery

We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made in the first stage. This class of problems finds many important applications in selection problems (e.g., in hiring, project portfolio optimization, or optimal sensor location). … Read more

Sample Average Approximation and Model Predictive Control for Multistage Stochastic Optimization

Sample average approximation-based stochastic dynamic programming and model predictive control are two different methods of approaching multistage stochastic optimization. Model predictive control—despite a lack of theoretical backing—is often used instead of stochastic dynamic programming due to computational necessity. For settings where the stage reward is a convex function of the random terms, the stage dynamics … Read more

It’s All in the Mix: Wasserstein Machine Learning with Mixed Features

Citation Belbasi R., Selvi A., Wiesemann W. (December 2023) It’s all in the mix: Wasserstein machine learning with mixed features. Preprint. Article Download View It's All in the Mix: Wasserstein Machine Learning with Mixed Features

Distributionally robust optimization through the lens of submodularity

Distributionally robust optimization is used to solve decision making problems under adversarial uncertainty where the distribution of the uncertainty is itself ambiguous. In this paper, we identify a class of these instances that is solvable in polynomial time by viewing it through the lens of submodularity. We show that the sharpest upper bound on the … Read more

Distributionally Risk-Receptive and Robust Multistage Stochastic Integer Programs and Two-player Interdiction Games with(out) Decision-Dependent Uncertainty

In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRA-MSIPs). These frameworks are useful for optimization problems under uncertainty where the focus is on analyzing outcomes based on multiple decision-makers’ differing perspectives, such as interdiction problems that are attacker-defender games having non-cooperative players. We … Read more

End-to-End Learning for Stochastic Optimization: A Bayesian Perspective

We develop a principled approach to end-to-end learning in stochastic optimization. First, we show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map. Building on the insights of this analysis, we then propose new end-to-end learning algorithms for training decision maps that output solutions of empirical risk … Read more