Abstract
Gaussian Process (GP) regression has seen widespread use in robotics due to its generality, simplicity of use, and the utility of Bayesian predictions. The predominant implementation of GP regression is a nonparametric kernel-based approach, as it enables fitting of arbitrary nonlinear functions. However, this approach suffers from two main drawbacks: (1) it is computationally inefficient, as computation scales poorly with the number of samples; and (2) it can be data inefficient, as encoding prior knowledge that can aid the model through the choice of kernel and associated hyperparameters is often challenging and unintuitive. 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 predictive density. These features are neural networks, which are trained via a meta-learning (or “learning-to-learn”) approach. ALPaCA extracts all prior information directly from the dataset, rather than restricting prior information to the choice of kernel hyperparameters. Furthermore, by operating in the weight space, it substantially reduces sample complexity. 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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Notes
- 1.
The code for all of our experiments is available at https://github.com/StanfordASL/ALPaCA.
- 2.
While the expressions in this work and [21] are not obviously equivalent, they can be shown to be the same by applying the Woodbury identity.
- 3.
Data available at: https://github.com/StanfordASL/TrafficWeavingCVAE.
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Acknowledgments
This work was supported by the Office of Naval Research YIP program (Grant N00014-17-1-2433), by DARPA under the Assured Autonomy program, and by the Toyota Research Institute (“TRI”). This article solely reflects the opinions and conclusions of its authors and not ONR, DARPA, TRI or any other Toyota entity. James Harrison was supported in part by the Stanford Graduate Fellowship and the National Sciences and Engineering Research Council (NSERC).
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Harrison, J., Sharma, A., Pavone, M. (2020). Meta-learning Priors for Efficient Online Bayesian Regression. In: Morales, M., Tapia, L., Sánchez-Ante, G., Hutchinson, S. (eds) Algorithmic Foundations of Robotics XIII. WAFR 2018. Springer Proceedings in Advanced Robotics, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-44051-0_19
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