Related papers: Optimal Regularization Under Uncertainty: Distribu…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…
As the complexity of modern control systems increases, it becomes challenging to derive an accurate model of the uncertainty that affects their dynamics. Wasserstein Distributionally Robust Optimization (DRO) provides a powerful framework…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
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…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
When solving rank-deficient or discrete ill-posed problems by regularization methods, the choice of the regularization parameter is crucial. It is also of interest, the regularization norm used in the selection of the solution. In this…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
Deep neural networks are the default choice of learning models for computer vision tasks. Extensive work has been carried out in recent years on explaining deep models for vision tasks such as classification. However, recent work has shown…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…
Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein…
This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…
We study a variety of Wasserstein distributionally robust optimization (WDRO) problems where the distributions in the ambiguity set are chosen by constraining their Wasserstein discrepancies to the empirical distribution. Using the notion…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Distributionally robust optimization tackles out-of-sample issues like overfitting and distribution shifts by adopting an adversarial approach over a range of possible data distributions, known as the ambiguity set. To balance conservatism…
Policy regularization methods such as maximum entropy regularization are widely used in reinforcement learning to improve the robustness of a learned policy. In this paper, we show how this robustness arises from hedging against worst-case…
Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although connection between…
We consider a minimax problem motivated by distributionally robust optimization (DRO) when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization…
In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the…
Robustness to adversarial attacks is an important concern due to the fragility of deep neural networks to small perturbations and has received an abundance of attention in recent years. Distributionally Robust Optimization (DRO), a…