Year: 2015
Type: article
Abstract: We extend the duality between exponential integrals and relative entropy to a variational formula for exponential integrals involving the Rényi divergence. This formula characterizes the dependence of risk-sensitive functionals to perturbations in the underlying distribution. It also shows that perturbations of related quantities determined by tail behavior, such as probabilities of rare events, can be bounded in terms of the Rényi divergence. The characterization gives rise to tight upper and lower bounds that are meaningful for all values of a large deviation scaling parameter, allowing one to quantify in explicit terms the robustness of risk-sensitive costs. As applications we consider problems of uncertainty quantification when aspects of the model are not fully known, as well their use in bounding tail properties of an intractable model in terms of a tractable one.
DOI: 10.1137/130939730
Authors: Rami Atar, Kenny Chowdhary, Paul Dupuis
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Awards: "NEW; LARGE DEVIATION METHODS FOR THE ANALYSIS AND DESIGN OF MONTE CARLO SCHEMES IN PHYSICS AND CHEMISTRY; PI - PAUL DUPUIS", G1339762611, Large Deviation Methods for the Analysis and Design of Accelerated Monte Carlo Schemes, G4255237535, MATHEMATICAL FOUNDATIONS FOR UNCERTAINTY QUANTIFICATION IN MATERIALS DESIGN
OpenAlex ID: W2139588953