Related papers: Optimal response for stochastic differential equat…
We consider optimal control problems for discrete-time random dynamical systems, finding unique perturbations that provoke maximal responses of statistical properties of the system. We treat systems whose transfer operator has an $L^2$…
We study stochastic differential equations on the $d$-dimensional flat torus $\mathbb{T}^d$ with drift and perturbation coefficients in $L^{\infty}(\mathbb{T}^d;\mathbb{R}^d)$ and additive non-degenerate noise. For the associated transfer…
In this paper, we introduce an adaptive kernel method for solving the optimal filtering problem. The computational framework that we adopt is the Bayesian filter, in which we recursively generate an optimal estimate for the state of a…
This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions,…
We consider the problem of optimal linear response for deterministic expanding maps of the circle. To each infinitesimal perturbation $\dot{T}$ of a circle map $T$ we consider (i) the response of the expectation of an observation function…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…
We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
I investigate the problem of optimally discriminating between two open quantum dynamical processes in a single-shot scenario, with the goal of minimizing the error probability of identification. This task involves optimising both the input…
We study the problem of optimal inside control of an SPDE (a stochastic evolution equation) driven by a Brownian motion and a Poisson random measure. Our optimal control problem is new in two ways: (i) The controller has access to inside…
Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information. We present a new derivation of the basic methodology, show…
Kernel embeddings of distributions have recently gained significant attention in the machine learning community as a data-driven technique for representing probability distributions. Broadly, these techniques enable efficient computation of…
Kernel Estimation is one of the most widely used estimation methods in non-parametric Statistics, having a wide-range of applications, including spot volatility estimation of stochastic processes. The selection of bandwidth and kernel…
In this paper we establish optimal regularity estimates and smoothness of free boundaries for nonlocal obstacle problems governed by a very general class of integro-differential operators with possibly singular kernels. More precisely, in…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
We present an empirical, gradient-based method for solving data-driven stochastic optimal control problems using the theory of kernel embeddings of distributions. By embedding the integral operator of a stochastic kernel in a reproducing…
The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…
In this paper the infinite horizon optimal regulation problem is solved online for a deterministic control-affine nonlinear dynamical system using the state following (StaF) kernel method to approximate the value function. Unlike…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…