On the design of LQR kernels for efficient controller learning

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Abstract

Finding optimal feedback controllers for nonlinear dynamic systems from data is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful framework for direct controller tuning from experimental trials. For selecting the next query point and finding the global optimum, BO relies on a probabilistic description of the latent objective function, typically a Gaussian process (GP). As is shown herein, GPs with a common kernel choice can, however, lead to poor learning outcomes on standard quadratic control problems. For a first-order system, we construct two kernels that specifically leverage the structure of the well-known Linear Quadratic Regulator (LQR), yet retain the flexibility of Bayesian nonparametric learning. Simulations of uncertain linear and nonlinear systems demonstrate that the LQR kernels yield superior learning performance.

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Marco, A., Hennig, P., Schaal, S., & Trimpe, S. (2018). On the design of LQR kernels for efficient controller learning. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (Vol. 2018-January, pp. 5193–5200). Institute of Electrical and Electronics Engineers Inc. https://doi.org/10.1109/CDC.2017.8264429

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