Triangle Inequality for Inverse Optimal Control

Inverse optimal control (IOC) is a problem of estimating a cost function based on the behaviors of an expert that behaves optimally with respect to the cost function. Although the Hamilton-Jacobi-Bellman (HJB) equation for the value function that evaluates the temporal integral of the cost function provides a necessary condition for the optimality of expert behaviors, the use of the HJB equation alone is insufficient for solving the IOC problem. In this study, we propose a triangle inequality which is useful for estimating the better representation of the value function, along with a new IOC method incorporating the triangle inequality. Through several IOC problems and imitation learning problems of time-dependent control behaviors, we show that our IOC method performs substantially better than an existing IOC method. Showing our IOC method is also applicable to an imitation of expert control of a 2-link manipulator, we demonstrate applicability of our method to real-world problems.