Related papers: Limit theorems for stochastic approximation algori…
We provide rates of convergence in the central limit theorem in terms of projective criteria for adapted stationary sequences of centered random variables taking values in Banach spaces, with finite moment of order $p \in ]2,3]$ as soon as…
The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
In this paper we prove a criterion of convergence in distribution in Skorokhod space. We apply this criterion to some special Levy processes and obtain almost-sure versions of limit theorems for these processes.
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
Distributed optimization algorithms have been studied extensively in the literature; however, underlying most algorithms is a linear consensus scheme, i.e. averaging variables from neighbors via doubly stochastic matrices. We consider…
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…
In this paper, we prove functional limit theorems for P\'olya urn processes whose number of draws and initial number of balls tend to infinity together. This is motivated by recent work of Borovkov [5], where they prove a functional limit…
We obtain explicit error bounds for the $d$-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a non-linear statistic of independent random…
The stratified resampling mechanism is one of the resampling schemes commonly used in the resampling steps of particle filters. In the present paper, we prove a central limit theorem for this mechanism under the assumption that the initial…
This paper studies linear stochastic approximation (SA) algorithms and their application to multi-agent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA…
Online averaged stochastic gradient algorithms are more and more studied since (i) they can deal quickly with large sample taking values in high dimensional spaces, (ii) they enable to treat data sequentially, (iii) they are known to be…
We study the statistical inference of nonlinear stochastic approximation algorithms utilizing a single trajectory of Markovian data. Our methodology has practical applications in various scenarios, such as Stochastic Gradient Descent (SGD)…
The proof of the theorem, which states that the Euclidean metric on the set of random points in an $n$-dimensional Euclidean space with the distribution of a special class, converges in probability in the limit $n\rightarrow\infty$ to the…
Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent results have shown that this can also be achieved in a…
Designing model-free algorithms for distributionally robust reinforcement learning (DRRL) poses fundamental challenges. The robust Bellman operator is nonlinear in the transition kernel, which makes one-sample Bellman updates biased, while…
We study k-median clustering under the sequential no-substitution setting. In this setting, a data stream is sequentially observed, and some of the points are selected by the algorithm as cluster centers. However, a point can be selected as…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
The discounted central limit theorem concerns the convergence of an infinite discounted sum of i.i.d. random variables to normality as the discount factor approaches $1$. We show that, using the Fourier metric on probability distributions,…