Online data assimilation in distributional robust optimization

Dan Li and Sonia Martínez
IEEE Transactions on Automatic Control, 66 (5) (2021) 2115-2129

Abstract:

This paper considers a class of real-time decision making problems to minimize the expected value of a function that depends on a random variable ξ under an unknown distribution ℙ. In this process, samples of ξ are collected sequentially in real time, and the decisions are made, using the real-time data, to guarantee out-of-sample performance. We approach this problem in a distributionally robust optimization framework and propose a novel Online Data Assimilation Algorithm for this purpose. This algorithm guarantees the out-of-sample performance in high probability, and gradually improves the quality of the data-driven decisions by incorporating the streaming data. We show that the Online Data Assimilation Algorithm guarantees convergence under the streaming data, and a criteria for termination of the algorithm after certain number of data has been collected.

File: (ArXiv version)

Bib-tex entry:

@article{DL-SM:21-tac,
author = {D. Li and S. Mart{\'\i}nez},
title = {Online data assimilation in distributional robust optimization},
journal= {IEEE Transactions on Automatic Control},
pages = {2115-2129},
volume = {66},
number = {5},
pages = {2115-2129},
year = {2021}
}