A Classification-based Approach for Approximate Reachability

Hamilton-Jacobi (HJ) reachability analysis has been developed over the past decades into a widely-applicable tool for determining goal satisfaction and safety verification in nonlinear systems. While HJ reachability can be formulated very generally, computational complexity can be a serious impediment for many systems of practical interest. Much prior work has been devoted to computing approximate solutions to large reachability problems, yet many of these methods may only apply to very restrictive problem classes, do not generate controllers, and/or can be extremely conservative. In this paper, we present a new method for approximating the optimal controller of the HJ reachability problem for control-affine systems. While also a specific problem class, many dynamical systems of interest are, or can be well approximated, by control-affine models. We explicitly avoid storing a representation of the reachability value function, and instead learn a controller as a sequence of simple binary classifiers. We compare our approach to existing grid-based methodologies in HJ reachability and demonstrate its utility on several examples, including a physical quadrotor navigation task

Expert Selection in High-Dimensional Markov Decision Processes

In this work we present a multi-armed bandit framework for online expert selection in Markov decision processes and demonstrate its use in high-dimensional settings. Our method takes a set of candidate expert policies and switches between them to rapidly identify the best performing expert using a variant of the classical upper confidence bound algorithm, thus ensuring low regret in the overall performance of the system. This is useful in applications where several expert policies may be available, and one needs to be selected at run-time for the underlying environment.Comment: In proceedings of the 59th IEEE Conference on Decision and Control 2020. arXiv admin note: text overlap with arXiv:1707.0571