相关论文: Approximation of *weak-to-norm continuous mappings
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
This paper establishes the nearly optimal rate of approximation for deep neural networks (DNNs) when applied to Korobov functions, effectively overcoming the curse of dimensionality. The approximation results presented in this paper are…
This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an estimator of the trace-class operator-valued integrated…
Norm estimates for strongly continuous semigroups have been successfully studied in numerous settings, but at the moment there are no corresponding studies in the case of solution operators of singular integral equations. Such equations…
We give a characterization of metric space valued Sobolev maps in terms of weak* derivatives. This corrects a previous result by Haj{\l}asz and Tyson.
The article is devoted to the development of numerical methods for solving variational inequalities with relatively strongly monotone operators. We consider two classes of variational inequalities related to some analogs of the Lipschitz…
We investigate the proximal map for the weighted mean absolute error function. An algorithm for its efficient and vectorized evaluation is presented. As a demonstration, this algorithm is applied as part of a checkerboard algorithm to solve…
In this work, we introduce new approximation operators for univariate set-valued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new…
In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a…
We study the application of Tikhonov regularization to ill-posed nonlinear operator equations. The objective of this work is to prove low order convergence rates for the discrepancy principle under low order source conditions of logarithmic…
In most practical applications of reinforcement learning, it is untenable to maintain direct estimates for individual states; in continuous-state systems, it is impossible. Instead, researchers often leverage state similarity (whether…
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial…
We study reinforcement learning methods with linear function approximation under non-Markov state and cost processes. We first consider the policy evaluation method and show that the algorithm converges under suitable ergodicity conditions…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
In this paper, we prove the rate of approximation for the Neural Network Sampling Operators activated by sigmoidal functions with mixed Lebesgue norm in terms of averaged modulus of smoothness for a bounded measurable functions on bounded…
In this note the Choquet type operators are introduced, in connection to Choquet's theory of integrability with respect to a not necessarily additive set function. Based on their properties, a quantitative estimate for the nonlinear…
We propose a fast, optimization-free method for learning the transition operators of high-dimensional Markov processes. The central idea is to perform a Galerkin projection of the transition operator to a suitable set of low-order bases…
We study critera for a pair $ (\{ X_n \} $, $ \{ Y_n \}) $ of approximating processes which guarantee closeness of moments by generalizing known results for the special case that $ Y_n = Y $ for all $n$ and $ X_n $ converges to $Y$ in…
In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative algorithm which gives rise to a…
Some results on the approximation of functions from the Sobolev spaces on metric graphs by step functions are obtained. The estimates are uniform with respect to all graphs of a given finite length, and the constant factors in the…