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Algorithmic machine teaching has been studied under the linear setting whereexact teaching is possible. However, little is known for teaching nonlinearlearners. Here, we establish the sample complexity of teaching, aka teachingdimension, for kernelized perceptrons for different families of feature maps.As a warm-up, we show that the teaching complexity is $\Theta(d)$ for the exactteaching of linear perceptrons in $\mathbb{R}^d$, and $\Theta(d^k)$ for kernelperceptron with a polynomial kernel of order $k$. Furthermore, under certainsmooth assumptions on the data distribution, we establish a rigorous bound onthe complexity for approximately teaching a Gaussian kernel perceptron. Weprovide numerical examples of the optimal (approximate) teaching set underseveral canonical settings for linear, polynomial and Gaussian kernelperceptrons.

The Teaching Dimension of Kernel Perceptron