Active Learning for Estimating Reachable Sets for Systems With Unknown Dynamics


This article presents a data-driven method for computing reachable sets that makes use of active learning (AL) to reduce the amount of work that needs to be done computationally. Methods that are based on sets and are used to estimate reachable sets typically do not scale well with the state-space dimension or place a heavy reliance on the presence of a model. If a model of this kind is not readily available, it is not difficult to generate data for state trajectories by numerically simulating black-box oracles of systems whose dynamics are unknown, starting with samples of the systems' initial conditions. Using these data samples, the estimation of reachable sets can be posed as a classification problem. Using artificial intelligence, AL can intelligently select samples that are most informative and least similar to samples that have been previously labeled. By taking advantage of submodularity, it is possible to select actively learned samples in an efficient manner, while maintaining bounded suboptimality. The estimation of the domains of attractions of model predictive controllers (MPCs) and reinforcement learners provides an illustration of the proposed framework that we have developed. We also take into consideration a scenario in which there are two oracles, each of which varies in terms of the costs of evaluation and the accuracy of labeling. Using disagreement-based AL, we propose a framework that will reduce the reliance on the costly oracle in the labeling of samples (DBAL). On a solver selection issue for real-time MPC, the potential of the DBAL algorithm is illustrated through a demonstration.

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