Data Assimilation and Online Optimization With Performance Guarantees

• 成果类型: Article
• 署名作者: Li, Dan; Martinez, Sonia
• 署名单位: University of California System; University of California San Diego
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3005681
• 发表日期: 2021
• 页码: 2115-2129
• 关键词: Optimization; uncertainty; Data assimilation; Random variables; probability distribution; Real-time systems; decision making; computational methods; Intelligent systems; optimization; optimization algorithms; Stochastic systems

摘要

This article considers a class of real-time stochastic optimization problems dependent on an unknown probability distribution. In the considered scenario, data are 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.