Dynamic evolution of distributional ambiguity sets and precision tradeoffs in data assimilation

Dimitris Boskos, Jorge Cortés and Sonia Martínez
Proceedings of the 18th European Control Conference, Naples, Italy, August 2019

Abstract:

This paper studies the evolution of ambiguity sets employed in distributionally robust optimization problems. We assume the unknown distribution of the random variable evolves according to a known deterministic dynamics. Assuming that the initial distribution of the data is compactly supported, we study how the assimilation of samples collected during some time interval evolution can be leveraged to make inferences about the unknown distribution of the process at the sampling horizon end. Under perfect knowledge of the dynamics' flow map, we provide sufficient conditions relating the solutions' growth and the sampling rate, which establish reduction of the ambiguity set size as the horizon increases. In the case where numerical errors are modeled during the computation of the flow, or the dynamics are subject to an unknown bounded disturbance, we also characterize the exploitable sample history that results in the guaranteed reduction of the ambiguity set.

File: main.pdf

Bib-tex entry:

@InProceedings{DB-JC-SM:19-ecc,
author = {D. Boskos and J. Cort\'es and S. Mart{\'\i}nez},
title = {Dynamic evolution of distributional ambiguity sets and precision tradeoffs in data assimilation},
booktitle = {18th European Control Conference},
pages = {},
year = {2019},
address = {Naples, Italy},
month = {June}
}