We consider modelling policies for MDPs in (vector-valued) reproducing kernel Hilbert function spaces (RKHS). This enables us to work “non-parametrically” in a rich function class, and provides the ability to learn complex policies. We present a framework for performing gradientbased policy optimization in the RKHS, deriving the functional gradient of the return for our policy, which has a simp...

A semiparametric model is a class of statistical models, which are characterized by a finite dimensional parameter and an infinite dimensional parameter. Asymptotic variance of estimator of the finite dimensional parameter is minimized when semiparametric efficient estimation is implemented. However, the efficient estimation is not possible for some models. We suggest a general method to carry ...

Variable selection is popular in high-dimensional data analysis to identify the truly informative variables. Many variable selection methods have been developed under various model assumptions. Whereas success has been widely reported in literature, their performances largely depend on validity of the assumed models, such as the linear or additive models. This article introduces a model-free va...

Kernel-target alignment is commonly used to predict the behavior of reproducing kernels in a classification context, without training any kernel machine. In this paper, we show that a poor position of training data in feature space can drastically reduce the value of alignment. This implies that, in a kernel selection setting, the best kernel of a given collection may be characterized by a low ...

We consider the problem of choosing a kernel suitable for estimation using a Gaussian Process estimator or a Support Vector Machine. A novel solution is presented which involves defining a Reproducing Kernel Hilbert Space on the space of kernels itself. By utilizing an analog of the classical representer theorem, the problem of choosing a kernel from a parameterized family of kernels (e.g. of v...