Simultaneous Optimization of Statistical Model and Control Input Plan

In this paper, we develop a simultaneous optimization problem of a statistical model and a control input plan. The aim of this problem is to obtain a high accuracy control input plan by using a statistical model with high generalization ability at important covariate values in determining a control input plan. We use covariate shift adaptation as the method to construct a statistical model. This enables us to construct the model with high generalization ability at a test distribution that is a specific covariate value's distribution. Concretely, we address a problem in which the controlled variable's prediction is improved by arbitrarily moving the test distribution. As the statistical model changes by covariate shift adaptation, the optimal plan of control inputs based on them also changes, so this problem becomes a problem of simultaneously optimizing the statistical model and the control input plan. To solve this problem, we propose an iterative alternate optimization method. We illustrate the effectiveness of the proposed method by using a simple numerical example of a charge/discharge plan problem of a storage battery.