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 AL-GORITHM 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.
This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite data-set of samples of the uncertain variables, we aim to find a data-driven solution that has a guaranteed out-of-sample performance. In principle, such formulation leads to an intractable problem (P) as the distribution of the uncertainty variable is unknown. By adopting a distributionally robust optimization approach, this work presents a tractable reformulation of (P) and an efficient algorithm that provides a suboptimal solution that retains the out-of-sample performance guarantee. A simulation illustrates the effectiveness of this method.
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