Random features for adaptive nonlinear control and prediction
- URL: http://arxiv.org/abs/2106.03589v1
- Date: Mon, 7 Jun 2021 13:15:40 GMT
- Title: Random features for adaptive nonlinear control and prediction
- Authors: Nicholas M. Boffi, Stephen Tu, Jean-Jacques E. Slotine
- Abstract summary: We propose a tractable algorithm for both adaptive control and adaptive prediction.
We approximate the unknown dynamics with a finite expansion in $textitrandom$ basis functions.
Remarkably, our explicit bounds only depend $textitpolynomially$ on the underlying parameters of the system.
- Score: 15.354147587211031
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A key assumption in the theory of adaptive control for nonlinear systems is
that the uncertainty of the system can be expressed in the linear span of a set
of known basis functions. While this assumption leads to efficient algorithms,
verifying it in practice can be difficult, particularly for complex systems.
Here we leverage connections between reproducing kernel Hilbert spaces, random
Fourier features, and universal approximation theory to propose a
computationally tractable algorithm for both adaptive control and adaptive
prediction that does not rely on a linearly parameterized unknown.
Specifically, we approximate the unknown dynamics with a finite expansion in
$\textit{random}$ basis functions, and provide an explicit guarantee on the
number of random features needed to track a desired trajectory with high
probability. Remarkably, our explicit bounds only depend
$\textit{polynomially}$ on the underlying parameters of the system, allowing
our proposed algorithms to efficiently scale to high-dimensional systems. We
study a setting where the unknown dynamics splits into a component that can be
modeled through available physical knowledge of the system and a component that
lives in a reproducing kernel Hilbert space. Our algorithms simultaneously
adapt over parameters for physical basis functions and random features to learn
both components of the dynamics online.
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