  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 nonparameteric 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.
