Meta-Learning Priors for Efficient Online Bayesian Regression
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Gaussian Process (GP) regression has seen widespread use in robotics due to its generality, simplicity of use, and the utility of Bayesian predictions. In particular, the predominant implementation of GP regression is kernel-based, as it enables fitting of arbitrary nonlinear functions by leveraging kernel functions as infinite-dimensional features. While incorporating prior information has the potential to drastically improve data efficiency of kernel-based GP regression, expressing complex priors through the choice of kernel function and associated hyperparameters is often challenging and unintuitive. Furthermore, the computational complexity of kernel-based GP regression scales poorly with the number of samples, limiting its application in regimes where a large amount of data is available. In this work, we propose ALPaCA, an algorithm for efficient Bayesian regression which addresses these issues. ALPaCA uses a dataset of sample functions to learn a domain-specific, finite-dimensional feature encoding, as well as a prior over the associated weights, such that Bayesian linear regression in this feature space yields accurate online predictions of the posterior density. These features are neural networks, which are trained via a meta-learning approach. ALPaCA extracts all prior information from the dataset, rather than relying on the choice of arbitrary, restrictive kernel hyperparameters. Furthermore, it substantially reduces sample complexity, and allows scaling to large systems. We investigate the performance of ALPaCA on two simple regression problems, two simulated robotic systems, and on a lane-change driving task performed by humans. We find our approach outperforms kernel-based GP regression, as well as state of the art meta-learning approaches, thereby providing a promising plug-in tool for many regression tasks in robotics where scalability and data-efficiency are important.
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