Related papers: Path Integral Control by Reproducing Kernel Hilber…

The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We…

We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…

We present a solution to the terminal-hitting stochastic reach-avoid problem for a Markov control process. This solution takes advantage of a nonparametric representation of the stochastic kernel as a conditional distribution embedding…

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…

The paper presents a novel learning-based sampling strategy that guarantees rejection-free sampling of the free space under both biased and approximately uniform conditions, leveraging multivariate kernel densities. Historical data from a…

The linear quadratic regulator problem is central in optimal control and was investigated since the very beginning of control theory. Nevertheless, when it includes affine state constraints, it remains very challenging from the classical…

We propose a representation of Gaussian processes (GPs) based on powers of the integral operator defined by a kernel function, we call these stochastic processes integral Gaussian processes (IGPs). Sample paths from IGPs are functions…

We develop a kernel-based solver for path-dependent PDEs (PPDEs) along with a convergence theory. Our numerical scheme leverages signature kernels, a recently introduced class of kernels on path-space. Specifically, we solve an optimal…

We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of non-linear control problems that can be formulated as a path integral and where the noise plays the role of…

Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…

This paper studies how to achieve accurate modeling and effective control in stochastic nonlinear dynamics with multiple interacting objects. However, non-uniform interactions and random topologies make this task challenging. We address…

In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…

Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…

In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…

Optimal control of switched systems is challenging due to the discrete nature of the switching control input. The embedding-based approach addresses this challenge by solving a corresponding relaxed optimal control problem with only…

Sampling-based controllers, such as Model Predictive Path Integral (MPPI) methods, offer substantial flexibility but often suffer from high variance and low sample efficiency. To address these challenges, we introduce a hybrid…

A nonparametric approach for policy learning for POMDPs is proposed. The approach represents distributions over the states, observations, and actions as embeddings in feature spaces, which are reproducing kernel Hilbert spaces.…

This paper presents a novel approach to formulating the actor-critic method for optimal control by casting policy iteration in reproducing kernel Hilbert spaces (RKHSs -- also known as native spaces). By tailoring the reproducing kernel and…

In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…

We generalize the derivation of model predictive path integral control (MPPI) to allow for a single joint distribution across controls in the control sequence. This reformation allows for the implementation of adaptive importance sampling…