Related papers: Robust optimization with belief functions

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…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…

Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become…

We address the problem of computing reliable policies in reinforcement learning problems with limited data. In particular, we compute policies that achieve good returns with high confidence when deployed. This objective, known as the…

In this work, we propose a novel method to tackle the problem of multiobjective optimization under parameteric uncertainties, by considering the Conditional Pareto Sets and Conditional Pareto Fronts. Based on those quantities we can define…

Prediction sets can wrap around any ML model to cover unknown test outcomes with a guaranteed probability. Yet, it remains unclear how to use them optimally for downstream decision-making. Here, we propose a decision-theoretic framework…

In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…

A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evidence. However, Shafer's theory of belief functions, which explicitly represents the underconstrained nature of many reasoning…

In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…

Robust optimization aims to find optimum points from the collection of points that are feasible for every possible scenario of a given uncertain set. An optimum solution to a robust optimization problem is commonly found by the min-max…

Addressing real-world optimization problems becomes particularly challenging when analytic objective functions or constraints are unavailable. While numerous studies have addressed the issue of unknown objectives, limited research has…

We consider global non-convex optimisation problems under uncertainty. In this setting, it is not possible to implement a desired solution exactly. Instead, any other solution within some distance to the intended solution may be…

Decision maker's preferences are often captured by some choice functions which are used to rank prospects. In this paper, we consider ambiguity in choice functions over a multi-attribute prospect space. Our main result is a robust…

Managing insurance and financial risk when data is limited is a key task in the insurance industry. In this paper, we focus on cases where the risk distribution is modeled as a mixture with some components estimable to high precision or…

The radius of robust feasibility provides a numerical value for the largest possible uncertainty set that guarantees robust feasibility of an uncertain linear conic program. This determines when the robust feasible set is non-empty.…

We provide sufficient conditions under which a utility function may be recovered from a finite choice experiment. Identification, as is commonly understood in decision theory, is not enough. We provide a general recoverability result that…

Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…

The paper deals with a lot sizing problem with ill-known demands modeled by fuzzy intervals whose membership functions are possibility distributions for the values of the uncertain demands. Optimization criteria, in the setting of…

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

Addressing uncertainty is critical for autonomous systems to robustly adapt to the real world. We formulate the problem of model uncertainty as a continuous Bayes-Adaptive Markov Decision Process (BAMDP), where an agent maintains a…