Related papers: Robustness certificates in data-driven non-convex …

A robustness certificate is the minimum distance of a given input to the decision boundary of the classifier (or its lower bound). For {\it any} input perturbations with a magnitude smaller than the certificate value, the classification…

In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…

We consider robust shortest path problems, where the aim is to find a path that optimizes the worst-case performance over an uncertainty set containing all relevant scenarios for arc costs. The usual approach for such problems is to assume…

Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…

In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is…

Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…

The literature on provable robustness in machine learning has primarily focused on static prediction problems, such as image classification, in which input samples are assumed to be independent and model performance is measured as an…

Robust optimization methods have shown practical advantages in a wide range of decision-making applications under uncertainty. Recently, their efficacy has been extended to multi-period settings. Current approaches model uncertainty either…

This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…

In this paper, we develop a two-stage data-driven approach to address the adjustable robust optimization problem, where the uncertainty set is adjustable to manage infeasibility caused by significant or poorly quantified uncertainties. In…

In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…

This work establishes a crucial step toward advancing data-driven trajectory-based methods for stochastic systems with unknown mathematical dynamics. In contrast to scenario-based approaches that rely on independent and identically…

Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…

Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances…

Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set. In the robust optimization framework the…

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness, while increasing the size of the…

In data-driven optimization, solution feasibility is often ensured through a "safe" reformulation of the uncertain constraints, such that an obtained data-driven solution is guaranteed to be feasible for the oracle formulation with high…

This article presents novel methods for synthesizing distributionally robust stabilizing neural controllers and certificates for control systems under model uncertainty. A key challenge in designing controllers with stability guarantees for…

This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number…

This paper develops a physics-informed scenario approach for safety verification of nonlinear systems using barrier certificates (BCs) to ensure that system trajectories remain within safe regions over an infinite time horizon. Designing…