Orateur
Description
We present a data-driven technique to automatically learn uncertainty sets in dynamic decision making under uncertainty. We formulate the learning problem as a control design problem where the control policy involves solving a robust optimization problem parametrized by the past disturbances, as well as the parameters of the uncertainty set. We propose a learning procedure to dynamically predict the parameters of the uncertainty set to minimize a closed-loop performance metric while satisfying probabilistic guarantees of constraint satisfaction. Our approach allows for uncertain data that is correlated across time periods, and can learn a wide range of commonly used uncertainty sets. By modeling our training problem objective and constraints using coherent risk metrics, we derive finite sample probabilistic guarantees of constraint satisfaction in multi-stage settings.
