Related papers: Local Limit Theorems and Strong Approximations for…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms…
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…
The Robbins-Siegmund theorem establishes the convergence of stochastic processes that are almost supermartingales and is one of the most commonly used approaches for analyzing stochastic iterative algorithms in stochastic approximation and…
We prove explicit, i.e., non-asymptotic, error bounds for Markov Chain Monte Carlo methods, such as the Metropolis algorithm. The problem is to compute the expectation (or integral) of f with respect to a measure which can be given by a…
In this paper, we consider the alleviation of the boundary problem when the probability density function has bounded support. We apply Robbins-Monro's algorithm and Bernstein polynomials to construct a recursive density estimator. We study…
Motivated by broad applications in reinforcement learning and federated learning, we study local stochastic approximation over a network of agents, where their goal is to find the root of an operator composed of the local operators at the…
Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…
Two time scale stochastic approximation algorithms emulate singularly perturbed deterministic differential equations in a certain limiting sense, i.e., the interpolated iterates on each time scale approach certain differential equations in…
This article presents a short and concise description of stochastic approximation algorithms in reinforcement learning of Markov decision processes. The algorithms can also be used as a suboptimal method for partially observed Markov…
In this paper, we propose a Robbins-Monro augmented Lagrangian method (RMALM) to solve a class of constrained stochastic convex optimization, which can be regarded as a hybrid of the Robbins-Monro type stochastic approximation method and…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local…
The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
We study Langevin-type algorithms for sampling from Gibbs distributions such that the potentials are dissipative and their weak gradients have finite moduli of continuity not necessarily convergent to zero. Our main result is a…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
This study introduces an iterative Bayesian Robbins--Monro (IBRM) sequence, which unites the classical Robbins--Monro sequence with statistical estimation for faster root-finding under noisy observations. Although the standard…
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…