Data assimilation and online optimization with performance guarantees
Abstract
This paper considers a class of real-time stochastic optimization problems dependent on an unknown probability distribution. In the considered scenario, data is streaming frequently while trying to reach a decision. Thus, we aim to devise a procedure that incorporates samples (data) of the distribution sequentially and adjusts decisions accordingly. We approach this problem in a distributionally robust optimization framework and propose a novel Online Data Assimilation Algorithm (ONDA Algorithm) for this purpose. This algorithm guarantees out-of-sample performance of decisions with high probability, and gradually improves the quality of the decisions by incorporating the streaming data. We show that the ONDA Algorithm converges under a sufficiently slow data streaming rate, and provide a criteria for its termination after certain number of data have been collected. Simulations illustrate the results.
Cite
@article{arxiv.1901.07377,
title = {Data assimilation and online optimization with performance guarantees},
author = {Dan Li and Sonia Martinez},
journal= {arXiv preprint arXiv:1901.07377},
year = {2020}
}
Comments
IEEE Transactions on Automatic Control. A preliminary work appeared in 10.1109/CDC.2018.8619159 and arxiv:1803.07984