Implicit Regularization and Momentum Algorithms in Nonlinearly Parameterized Adaptive Control and Prediction
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neco_a_01360.pdf
Description
Published version
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2.7 MB
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Adobe PDF
Checksum (MD5)
3a0e7c093c291d0ecb0a1be7f832f81c
Author(s)
Boffi, Nicholas M
Slotine, Jean-Jacques E
Date Issued
2021
Journal
Neural Computation
Publisher
MIT Press - Journals
Citation
Boffi, Nicholas M and Slotine, Jean-Jacques E. 2021. "Implicit Regularization and Momentum Algorithms in Nonlinearly Parameterized Adaptive Control and Prediction." Neural Computation, 33 (3).
Version
Final published version
Abstract
Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear systems revolves around a few key algorithms. By exploiting strong connections between classical adaptive nonlinear control techniques and recent progress in optimization and machine learning, we show that there exists considerable untapped potential in algorithm development for both adaptive nonlinear control and adaptive dynamics prediction. We begin by introducing first-order adaptation laws inspired by natural gradient descent and mirror descent. We prove that when there are multiple dynamics consistent with the data, these non-Euclidean adaptation laws implicitly regularize the learned model. Local geometry imposed during learning thus may be used to select parameter vectors—out of the many that will achieve perfect tracking or prediction—for desired properties such as sparsity. We apply this result to regularized dynamics predictor and observer design, and as concrete examples, we consider Hamiltonian systems, Lagrangian systems, and recurrent neural networks. We subsequently develop a variational formalism based on the Bregman Lagrangian. We show that its Euler Lagrange equations lead to natural gradient and mirror descent-like adaptation laws with momentum, and we recover their first-order analogues in the infinite friction limit. We illustrate our analyses with simulations demonstrating our theoretical results.
MIT Department
Massachusetts Institute of Technology. Nonlinear Systems Laboratory
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1162/NECO_A_01360
