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We develop algorithms with low regret for learning episodic Markov decision processes based on kernel approximation techniques. The algorithms are based on both the Upper Confidence Bound (UCB) as well as Posterior or Thompson Sampling…
Emerging applications increasingly demand flexible covariate adaptive randomization (CAR) methods that support unequal targeted allocation ratios. While existing procedures can achieve covariate balance, they often suffer from the shift…
Kolmogorov-Arnold Networks (KANs) offer a structured and interpretable framework for multivariate function approximation by composing univariate transformations through additive or multiplicative aggregation. This paper establishes…
We propose an algorithm, based on Algebraic Renormalization, that allows the restoration of Slavnov-Taylor invariance at every order of perturbation expansion for an anomaly-free BRS invariant gauge theory. The counterterms are explicitly…
In applications, a substantial number of problems can be formulated as non-linear least squares problems over smooth varieties. Unlike the usual least squares problem over a Euclidean space, the non-linear least squares problem over a…
Let $P$ be a Markov kernel on a measurable space $\X$ and let $V:\X\r[1,+\infty)$. We provide various assumptions, based on drift conditions, under which $P$ is quasi-compact on the weighted-supremum Banach space $(\cB_V,\|\cdot\|_V)$ of…
We show that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems provided that a parameter is chosen accordingly to the smoothness of the solution. This result is proven both for an a…
In this paper, we investigate very general approximation kernels with special properties, called an approximate identity, and prove almost everywhere and norm convergence of these general methods, which consists of a class of summability…
Over the past decade, a combinatorial framework for discrete, finite, and irreversibly aggregating systems has emerged. This work reviews its progress, practical applications, and limitations. We outline the approach's assumptions and…
Narayana numbers appear in many places in combinatorics and probability, and it is known that they are asymptotically normal. Using Stein's method of exchangeable pairs, we provide an error of approximation in total variation to a symmetric…
Randomized controlled trials (RCTs) frequently utilize covariate-adaptive randomization (CAR) (e.g., stratified block randomization) and commonly suffer from imperfect compliance. This paper studies the identification and inference for the…
This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the…
In this work, we broadly connect kernel-based filtering (e.g. approaches such as the bilateral filters and nonlocal means, but also many more) with general variational formulations of Bayesian regularized least squares, and the related…
Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of $k$ arguments is assumed to be continuous with…
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…
The recently developed average-case analysis of optimization methods allows a more fine-grained and representative convergence analysis than usual worst-case results. In exchange, this analysis requires a more precise hypothesis over the…
We present the modified approach to the classical Bogolyubov-Krylov averaging, developed recently for the purpose of PDEs. It allows to treat Lipschitz perturbations of linear systems with pure imaginary spectrum and may be generalized to…
In recent years, significant attention has been directed towards learning average-reward Markov Decision Processes (MDPs). However, existing algorithms either suffer from sub-optimal regret guarantees or computational inefficiencies. In…