Abstract Inverse optimal control (IOC) is a powerful approach for learning robotic controllers from demonstration that estimates a cost function which rationalizes demonstrated control trajectories. Unfortunately, its applicability is diffificult in settings where optimal control can only be solved approximately. While local IOC approaches have been shown to successfully learn cost functions in such settings, they rely on the availability of good reference trajectories, which might not be available at test time. We address the problem of using IOC in these computationally challenging control tasks by using a graph-based discretization of the trajectory space. Our approach projects continuous demonstrations onto this discrete graph, where a cost function can be tractably learned via IOC. Discrete control trajectories from the graph are then projected back to the original space and locally optimized using the learned cost function. We demonstrate the effectiveness of the approach with experiments conducted on two 7-degree of freedom robotic arms