Meta-learning Priors for Efficient Online Bayesian Regression

Harrison, J. Michael; Sharma, Anita; Pavone, Marco

doi:10.1007/978-3-030-44051-0_19

Cited by 53 publications

(72 citation statements)

References 16 publications

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“…O'Connell et al [55] apply this same method to learn neural network features for nonlinear mechanical systems. Harrison et al [28,27] more generally back-propagate through a Bayesian regression solution to train a Bayesian prior dynamics model with nonlinear features. Nagabandi et al [50] use a maximum likelihood meta-objective, and gradient descent on a multi-step likelihood objective as the base-learner.…”

Section: Meta-learningmentioning

confidence: 99%

“…Adaptive Control via Meta-Ridge Regression (ACMRR): This baseline is a slightly modified 1 version of the approach taken by O'Connell et al [55], which applies the work on using ridge regression as a base-learner from Bertinetto et al [11], Lee et al [42] and Harrison et al [28] to learn the parametric features y(q,q; θ y ). Specifically, for a given trajectory T j and these features, the last layer A is specified as the best ridge regression fit to some subset of points in T j .…”

Section: A Baselinesmentioning

confidence: 99%

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Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems

Richards

Azizan

Slotine

et al. 2021

Robotics: Science and Systems XVII

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Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics terms are linearly parameterizable with known nonlinear features. However, it is often difficult to specify such features a priori, such as for aerodynamic disturbances on rotorcraft or interaction forces between a manipulator arm and various objects. In this paper, we turn to data-driven modeling with neural networks to learn, offline from past data, an adaptive controller with an internal parametric model of these nonlinear features.Our key insight is that we can better prepare the controller for deployment with control-oriented meta-learning of features in closed-loop simulation, rather than regression-oriented metalearning of features to fit input-output data. Specifically, we metalearn the adaptive controller with closed-loop tracking simulation as the base-learner and the average tracking error as the metaobjective. With a nonlinear planar rotorcraft subject to wind, we demonstrate that our adaptive controller outperforms other controllers trained with regression-oriented meta-learning when deployed in closed-loop for trajectory tracking control.

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Section: Meta-learningmentioning

confidence: 99%

Section: A Baselinesmentioning

confidence: 99%

Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems

Richards

Azizan

Slotine

et al. 2021

Robotics: Science and Systems XVII

Self Cite

View full text Add to dashboard Cite

show abstract

“…Integrating uncertainty has typically been achieved by learning probabilistic dynamics models from collected statetransition data in an episodic setting, where the model is updated in between trajectory-length system executions [7,22,35,28]. A variety of modelling representations have been explored, including Gaussian processes [8], neural network ensembles [7], Bayesian regression, and meta-learning [16]. Alternatively, the authors in [28,26] estimate posterior distributions of physical parameters for black-box simulators, given real-world observations.…”

Section: Related Workmentioning

confidence: 99%

Dual Online Stein Variational Inference for Control and Dynamics

Barcelos¹,

Lambert²,

Oliveira³

et al. 2021

Robotics: Science and Systems XVII

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Model predictive control (MPC) schemes have a proven track record for delivering aggressive and robust performance in many challenging control tasks, coping with nonlinear system dynamics, constraints, and observational noise. Despite their success, these methods often rely on simple control distributions, which can limit their performance in highly uncertain and complex environments. MPC frameworks must be able to accommodate changing distributions over system parameters, based on the most recent measurements. In this paper, we devise an implicit variational inference algorithm able to estimate distributions over model parameters and control inputs on-the-fly. The method incorporates Stein Variational gradient descent to approximate the target distributions as a collection of particles, and performs updates based on a Bayesian formulation. This enables the approximation of complex multi-modal posterior distributions, typically occurring in challenging and realistic robot navigation tasks. We demonstrate our approach on both simulated and realworld experiments requiring real-time execution in the face of dynamically changing environments.

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“…A classical way of meta-learning with a stochastic process would be the Bayesian last layer (BLL) method (Weber et al 2018;Harrison, Sharma, and Pavone 2018), which fits into the former way of defining the task. Using the fact that the last layers of many neural networks are usually (generalized) linear models, a straightforward way of building a flexible stochastic process is to set a Gaussian prior on the weights of the last layer.…”

Section: Bayesian Last Layer (Bll)mentioning

confidence: 99%

“…In this paper, we delve further into the structural similarity between the ANPs and traditional stochastic processes, namely the Bayesian last layer (BLL) (Calandra et al 2016;Weber et al 2018;Harrison, Sharma, and Pavone 2018), as ANPs are designed to mimic BLL's behavior efficiently. It turns out that the self-attention layers in an ANP are not expressive enough, and simple cases where the underlying functions lie in the space spanned by a feature extractor, which can be exactly modeled with BLL, might not be efficiently learned.…”

Section: Introductionmentioning

confidence: 99%

Residual Neural Processes

Lee

Hong

Kim

2020

AAAI

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A Neural Process (NP) is a map from a set of observed input-output pairs to a predictive distribution over functions, which is designed to mimic other stochastic processes' inference mechanisms. NPs are shown to work effectively in tasks that require complex distributions, where traditional stochastic processes struggle, e.g. image completion tasks. This paper concerns the practical capacity of set function approximators despite their universality. By delving deeper into the relationship between an NP and a Bayesian last layer (BLL), it is possible to see that NPs may struggle in simple examples, which other stochastic processes can easily solve. In this paper, we propose a simple yet effective remedy; the Residual Neural Process (RNP) that leverages traditional BLL for faster training and better prediction. We demonstrate that the RNP shows faster convergence and better performance, both qualitatively and quantitatively.

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Meta-learning Priors for Efficient Online Bayesian Regression

Cited by 53 publications

References 16 publications

Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems

Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems

Dual Online Stein Variational Inference for Control and Dynamics

Residual Neural Processes

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