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We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

This paper studies a robust utility maximization problem for intractable claims under distributional ambiguity, where the distribution of the claim cannot be inferred from market information and its dependence with tradable assets is…

We review distributionally robust optimization (DRO), a principled approach for constructing statistical estimators that hedge against the impact of deviations in the expected loss between the training and deployment environments. Many…

This paper studies distributionally robust optimization (DRO) with polynomial robust constraints. We give a Moment-SOS relaxation approach to solve the DRO. This reduces to solving linear conic optimization with semidefinite constraints.…

We consider a real-world chemotherapy scheduling template design problem, where we cluster patient types into groups and find a representative time-slot duration for each group to accommodate all patient types assigned to that group, aiming…

In this paper, we consider the resource allocation problem in a network with a large number of connections which are used by a huge number of users. The resource allocation problem under discussion is a maximization problem with linear…

Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of…

In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…

Real-world deployments routinely face distribution shifts, group imbalances, and adversarial perturbations, under which the traditional Empirical Risk Minimization (ERM) framework can degrade severely. Distributionally Robust Optimization…

A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and…

In this paper, we provide different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distributions. The first method involves computing the proximity…

Data-driven Distributionally Robust Optimization (DD-DRO) via optimal transport has been shown to encompass a wide range of popular machine learning algorithms. The distributional uncertainty size is often shown to correspond to the…

This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More…

Robust optimization (RO) tackles data uncertainty by optimizing for the worst-case scenario of an uncertain parameter and, in its basic form, is sometimes criticized for producing overly-conservative solutions. To reduce the level of…

Recently, (Blanchet, Kang, and Murhy 2016, and Blanchet, and Kang 2017) showed that several machine learning algorithms, such as square-root Lasso, Support Vector Machines, and regularized logistic regression, among many others, can be…

We analyze the axiomatic properties of a class of probability estimators derived from Distributionally Robust Optimization (DRO) with $q$-norm ambiguity sets ($q$-DRO), a principled approach to the zero-frequency problem. While classical…

In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $\phi$-divergences and Wasserstein distances, respectively. While the former focuses on ambiguity in…

This paper focuses on solving a data-driven distributionally robust optimization problem over a network of agents. The agents aim to minimize the worst-case expected cost computed over a Wasserstein ambiguity set that is centered at the…

We propose a novel methodology for solving a two-stage adjustable robust convex optimisation problem with a general (proximable) convex objective function and constraints defined by sum-of-squares (SOS) convex polynomials. These problems…