Related papers: Data-Driven Chance Constrained Optimization under …

Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…

In problems that involve input parameter information gathered from multiple data sources with varying reliability, incorporating decision makers' trust on different sources in optimization models can potentially improve solution…

We consider decision-making problems under decision-dependent uncertainty (DDU), where the distribution of uncertain parameters depends on the decision variables and is only observable through a finite offline dataset. To address this…

Many real-world decision-making problems have uncertain parameters in constraints. Wasserstein distributionally robust joint chance constraints (WDRJCC) offer a promising solution by explicitly guaranteeing the probability of the…

A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…

Data-driven machine learning methodologies have attracted considerable attention for the control and estimation of dynamical systems. However, such implementations suffer from a lack of predictability and robustness. Thus, adoption of…

This paper studies a data-driven predictive control for a class of control-affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are…

In this work, we develop a novel data-driven Bayesian nonparametric Wasserstein distributionally robust optimization (BNWDRO) framework for decision-making under uncertainty. The proposed framework unifies a Bayesian nonparametric method…

We study sample average approximations (SAA) of chance constrained programs. SAA methods typically approximate the actual distribution in the chance constraint using an empirical distribution constructed from random samples assumed to be…

Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their…

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If…

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…

Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…

Distributed model predictive control methods for uncertain systems often suffer from considerable conservatism and can tolerate only small uncertainties due to the use of robust formulations that are amenable to distributed design and…

The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…

We consider a class of stochastic interdiction games between an upper-level decision-maker (the leader) and a lower-level decision-maker (the follower), where uncertainty lies in the follower's objective function coefficients. Specifically,…

Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. This paper introduces a novel formalism for a prominent problem in…

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…

In this work, we study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity. Our approach builds on a backup-based safety filtering framework that switches between a high-performance nominal policy and a…

Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…