Multi-Level Multi-Fidelity Methods for Path Integral and Safe Control

Sampling-based approaches are widely used in systems without analytic models to estimate risk or find optimal control. However, gathering sufficient data in such scenarios can be prohibitively costly. On the other hand, in many situations, low-fidelity models or simulators are available from which samples can be obtained at low cost. In this paper, we propose an efficient approach for risk quantification and path integral control that leverages such data from multiple models with heterogeneous sampling costs. A key technical novelty of our approach is the integration of Multi-level Monte Carlo (MLMC) and Multi-fidelity Monte Carlo (MFMC) that enable data from different time and state representations (system models) to be jointly used to reduce variance and improve sampling efficiency. We also provide theoretical analysis of the proposed method and show that our estimator is unbiased and consistent under mild conditions. Finally, we demonstrate via numerical simulation that the proposed method has improved computation (sampling costs) vs. accuracy trade-offs for risk quantification and path integral control.