Online data assimilation in distributionally robust optimization

Dan Li and Sonia Martínez
Proceedings of the 57th IEEE Int. Conference on Decision and Control, Miami, FL, USA, December 2018

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 xi under an unknown distribution P. In this process, samples of xi 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: main.pdf

Bib-tex entry:

@InProceedings{DL-SM,
author = {D. Li and S. Mart{\'\i}nez},
title = {Online data assimilation in distributionally robust optimization},
booktitle = {57th IEEE International Conference on Decision and Control},
pages = {1961--1966},
year = {2018},
address = {Miami, FL, USA},
month = {December}
}