Stochastic and robust optimization constitute natural frameworks to solve decision-making and control problems subject to uncertainty. However, these fall short in addressing real-world scenarios for which models of the uncertainty are not available. Data-driven approaches can be of help to approximate such models, but typically require large amounts of data in order to produce performance-guaranteed results. Motivated by settings where the collection of data is costly and fast decisions need to be made online, we present recent work on the construction of dynamic ambiguity sets for uncertainties that evolves according to a dynamical law. In particular, we characterize the tradeoffs between the amount of progressively assimilated data and its future adequacy, due to its gradual precision loss in its predicted values.
Data-driven Dynamic Ambiguity Sets: Precision Tradeoffs under Noisy Measurements
Sonia Martinez, University of California, San Diego
2022 AWM Research Symposium
Systems and Control