Robust and Distributionally Robust Optimization Models for Support Vector Machine

In this paper we present novel data-driven optimization models for Support Vector Machines (SVM), with the aim of linearly separating two sets of points that have non-disjoint convex closures. Traditional classi cation algorithms assume that the training data points are always known exactly. However, real-life data are often subject to noise. To handle such uncertainty, we … Read more

Vessel Deployment with Limited Information: Distributionally Robust Chance Constrained Models

This paper studies the fundamental vessel deployment problem in the liner shipping industry, which decides the numbers of mixed-type ships and their sailing frequencies on fixed routes to provide sufficient vessel capacity for fulfilling stochastic shipping demands with high probability. In reality, it is usually difficult (if not impossible) to acquire a precise joint distribution … Read more

Heteroscedasticity-aware residuals-based contextual stochastic optimization

We explore generalizations of some integrated learning and optimization frameworks for data-driven contextual stochastic optimization that can adapt to heteroscedasticity. We identify conditions on the stochastic program, data generation process, and the prediction setup under which these generalizations possess asymptotic and finite sample guarantees for a class of stochastic programs, including two-stage stochastic mixed-integer programs … Read more

Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications

We consider a general conic mixed-binary set where each homogeneous conic constraint involves an affine function of independent continuous variables and an epigraph variable associated with a nonnegative function, $f_j$, of common binary variables. Sets of this form naturally arise as substructures in a number of applications including mean-risk optimization, chance-constrained problems, portfolio optimization, lot-sizing … Read more

Data-Driven Optimization with Distributionally Robust Second-Order Stochastic Dominance Constraints

Optimization with stochastic dominance constraints has recently received an increasing amount of attention in the quantitative risk management literature. Instead of requiring that the probabilistic description of the uncertain parameters be exactly known, this paper presents the first comprehensive study of a data-driven formulation of the distributionally robust second-order stochastic dominance constrained problem (DRSSDCP) that … Read more

Kernel Distributionally Robust Optimization

We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct a wide range of convex ambiguity sets, including sets based on integral probability metrics and finite-order moment bounds. This perspective unifies multiple existing robust and stochastic optimization … Read more

Residuals-based distributionally robust optimization with covariate information

We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained … Read more

A Distributionally-Robust Service Center Location Problem with Decision Dependent Demand Induced from a Maximum Attraction Principle

We establish and analyze a service center location model with a simple but novel decision-dependent demand induced from a maximum attrac- tion principle. The model formulations are investigated in the distributionally- robust optimization framework. A statistical model that is based on the max- imum attraction principle for estimating customer demand and utility gain from service … Read more

A Novel Solution Methodology for Wasserstein-based Data-Driven Distributionally Robust Problems

Distributionally robust optimization (DRO) is a mathematical framework to incorporate ambiguity over the actual data-generating probability distribution. Data-driven DRO problems based on the Wasserstein distance are of particular interest for their sound mathematical properties. For right-hand-sided uncertainty, however, existing methods rely on dual vertex enumeration rendering the problem intractable in practical applications. In this context, … Read more

Distributionally Robust Two-Stage Stochastic Programming

Distributionally robust optimization is a popular modeling paradigm in which the underlying distribution of the random parameters in a stochastic optimization model is unknown. Therefore, hedging against a range of distributions, properly characterized in an ambiguity set, is of interest. We study two-stage stochastic programs with linear recourse in the context of distributional ambiguity, and … Read more