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Meta Learning MPC using Finite-Dimensional Gaussian Process Approximations

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Document pages: 10 pages

Abstract: Data availability has dramatically increased in recent years, drivingmodel-based control methods to exploit learning techniques for improving thesystem description, and thus control performance. Two key factors that hinderthe practical applicability of learning methods in control are their highcomputational complexity and limited generalization capabilities to unseenconditions. Meta-learning is a powerful tool that enables efficient learningacross a finite set of related tasks, easing adaptation to new unseen tasks.This paper makes use of a meta-learning approach for adaptive model predictivecontrol, by learning a system model that leverages data from previous relatedtasks, while enabling fast fine-tuning to the current task during closed-loopoperation. The dynamics is modeled via Gaussian process regression and,building on the Karhunen-Lo{è}ve expansion, can be approximately reformulatedas a finite linear combination of kernel eigenfunctions. Using data collectedover a set of tasks, the eigenfunction hyperparameters are optimized in ameta-training phase by maximizing a variational bound for the log-marginallikelihood. During meta-testing, the eigenfunctions are fixed, so that only thelinear parameters are adapted to the new unseen task in an online adaptivefashion via Bayesian linear regression, providing a simple and efficientinference scheme. Simulation results are provided for autonomous racing withminiature race cars adapting to unseen road conditions.

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