Related papers: Smooth Uncertainty Sets: Dependence of Uncertain P…
In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…
Applying robust optimization often requires selecting an appropriate uncertainty set both in shape and size, a choice that directly affects the trade-off between average-case and worst-case performances. In practice, this calibration is…
Distributionally robust optimization (DRO) incorporates robustness against uncertainty in the specification of probabilistic models. This paper focuses on mitigating the curse of dimensionality in data-driven DRO problems with optimal…
Interest has been growing in decision-focused machine learning methods which train models to account for how their predictions are used in downstream optimization problems. Doing so can often improve performance on subsequent decision…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
When a machine learning model is deployed, its predictions can alter its environment, as better informed agents strategize to suit their own interests. With such alterations in mind, existing approaches to uncertainty quantification break.…
In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, 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…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that…
This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse…
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…
Decision-making problems can be modeled as combinatorial optimization problems with Constraint Programming formalisms such as Constrained Optimization Problems. However, few Constraint Programming formalisms can deal with both optimization…
This work considers the optimal covariance steering problem for systems subject to both additive noise and uncertain parameters which may enter multiplicatively with the state and the control. The unknown parameters are modeled as a…
Robust optimization safeguards decisions against uncertainty by optimizing against worst-case scenarios, yet their effectiveness hinges on a prespecified robustness level that is often chosen ad hoc, leading to either insufficient…
We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this…
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…
Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an…