Related papers: Statistics of Robust Optimization: A Generalized E…

We consider a discrete time stochastic Markovian control problem under model uncertainty. Such uncertainty not only comes from the fact that the true probability law of the underlying stochastic process is unknown, but the parametric family…

We propose a data-driven technique to automatically learn contextual uncertainty sets in robust optimization, resulting in excellent worst-case and average-case performance while also guaranteeing constraint satisfaction. Our method…

Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…

We propose a distributionally robust formulation of the traditional risk parity portfolio optimization problem. Distributional robustness is introduced by targeting the discrete probabilities attached to each observation used during…

This work presents a new Distributionally Robust Optimization approach, using $p$-Wasserstein metrics, to analyze a stochastic program in a general context. The ambiguity set in this approach depends on the decision variable and is…

We study control of constrained linear systems with only partial statistical information about the uncertainty affecting the system dynamics and the sensor measurements. Specifically, given a finite collection of disturbance realizations…

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…

In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…

Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…

Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…

This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…

We study a methodology to tackle the NASA Langley Uncertainty Quantification Challenge problem, based on an integration of robust optimization, more specifically a recent line of research known as distributionally robust optimization, and…

We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…

We study robust estimators of the mean of a probability measure $P$, called robust empirical mean estimators. This elementary construction is then used to revisit a problem of aggregation and a problem of estimator selection, extending…

Most signal processing and statistical applications heavily rely on specific data distribution models. The Gaussian distributions, although being the most common choice, are inadequate in most real world scenarios as they fail to account…

We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…

A new variant of Newton's method for empirical risk minimization is studied, where at each iteration of the optimization algorithm, the gradient and Hessian of the objective function are replaced by robust estimators taken from existing…

Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating…