7. Juni 2022
Sebastian Court (Universität Innsbruck)
Title: Relaxation Approach for Learning Regularizers by Neural Networks for a Class of Optimal Control Problems
Abstract:
We propose a data-driven design of regularizers in the form of artificial neural networks for solving inverse problems formulated as optimal control problems. These regularizers aim at improving accuracy and stability, or compensating uncertainties for a class of optimal control problems (inner-problems). Parameterized as neural networks, their weights are chosen in order to reduce a misfit between data and observations of a state solution of the underlying optimal control problem. Learning these weights constitutes the outer-problem. Based on necessary first-order optimality conditions for the inner-problems, a relaxation approach is proposed in order to implement efficient solving of the inner-problems, namely the forward operator of the outer-problem. Optimality conditions are then derived for the latter, and numerical illustrations show the feasibility of the relaxation approach, for instance for designing regularizers that compensate unknown noise on the observed state of the inner-problem.