Related papers: Tailoring Reproducing Kernels for Optimal Control …
Learning optimal behavior from existing data is one of the most important problems in Reinforcement Learning (RL). This is known as "off-policy control" in RL where an agent's objective is to compute an optimal policy based on the data…
For three applications of central interest in finance, we demonstrate the relevance of numerical algorithms based on reproducing kernel Hilbert space (RKHS) techniques. Three use cases are investigated. First, we show that extrapolating…
Integral operators play a central role in signal processing, underpinning classical convolution, and filtering on continuous network models such as graphons. While these operators are traditionally analyzed through spectral decompositions,…
We develop a rigorous framework for extending neural operators to handle out-of-distribution input functions. We leverage kernel approximation techniques and provide theory for characterizing the input-output function spaces in terms of…
Interest in reinforcement learning (RL) for large-scale systems, comprising extensive populations of intelligent agents interacting with heterogeneous environments, has surged significantly across diverse scientific domains in recent years.…
This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…
Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to certain Sobolev spaces. In the context of interpolation, the…
In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the…
Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…
An extension of reproducing kernel Hilbert space (RKHS) theory provides a new framework for modeling functional regression models with functional responses. The approach only presumes a general nonlinear regression structure as opposed to…
Active policy search combines the trial-and-error methodology from policy search with Bayesian optimization to actively find the optimal policy. First, policy search is a type of reinforcement learning which has become very popular for…
We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic…
Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring…
Optimization of parameterized policies for reinforcement learning (RL) is an important and challenging problem in artificial intelligence. Among the most common approaches are algorithms based on gradient ascent of a score function…
Model predictive control allows solving complex control tasks with control and state constraints. However, an optimal control problem must be solved in real-time to predict the future system behavior, which is hardly possible on embedded…
We study recursive regularized learning algorithms in the reproducing kernel Hilbert space (RKHS) with non-stationary online data streams. We introduce the concept of random Tikhonov regularization path and decompose the tracking error of…
Radial basis functions (RBFs) are prominent examples for reproducing kernels with associated reproducing kernel Hilbert spaces (RKHSs). The convergence theory for the kernel-based interpolation in that space is well understood and optimal…
We consider a kernelized bandit problem with a compact arm set ${X} \subset \mathbb{R}^d $ and a fixed but unknown reward function $f^*$ with a finite norm in some Reproducing Kernel Hilbert Space (RKHS). We propose a class of…
We consider both discrete and continuous control problems constrained by a fixed budget of some resource, which may be renewed upon entering a preferred subset of the state space. In the discrete case, we consider both deterministic and…