Structure Determination of a Criterion Function by Dynamic Inverse Optimization

In this paper, we propose a novel approach to dynamic inverse optimization by the learning of neural networks. A dynamic inverse optimization problem here means to estimate a criterion function under which given input and output sequences become optimal for a known state equation model. A neural network architecture representing the optimality condition including an algebraic Riccati equation is proposed for solving dynamic inverse optimization problems. Also proposed is the determination of the structure of a criterion function by the statistical test, i.e., which state variables are included in a criterion function based on data contaminated by additive noise. Applications of the proposed method to given input and output sequences contaminated by observation noise well demonstrate its e ectiveness.