Inverse KKT: Learning cost functions of manipulation tasks from demonstrations

Inverse Optimal Control (IOC) assumes that demonstrations are the solution to an optimal control problem with unknown underlying costs, and extracts parameters of these underlying costs. We propose the framework of Inverse KKT, which assumes that the demonstrations fulfill the Karush-Kuhn-Tucker conditions of an unknown underlying constrained optimization problem, and extracts parameters of this underlying problem. Using this we can exploit the latter to extract the relevant task spaces and cost parameters from demonstrations of skills that involve contacts. For a typical linear parameterization of cost functions this reduces to a quadratic program, ensuring guaranteed and very efficient convergence, but we can deal also with arbitrary non-linear parameterizations of cost functions. The aim of our approach is to push learning from demonstration to more complex manipulation scenarios that include the interaction with objects and therefore the realization of contacts/constraints within the motion. We demonstrate the approach on tasks such as sliding a box and opening a door.