Related papers: Statistical Inference for Polyak-Ruppert Averaged …

This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…

This paper derives non-asymptotic error bounds for nonlinear stochastic approximation algorithms in the Wasserstein-$p$ distance. To obtain explicit finite-sample guarantees for the last iterate, we develop a coupling argument that compares…

In this article we establish new central limit theorems for Ruppert-Polyak averaged stochastic gradient descent schemes. Compared to previous work we do not assume that convergence occurs to an isolated attractor but instead allow…

Finding effective ways to exploit parallel computing to accelerate Markov chain Monte Carlo methods is an important problem in Bayesian computation and related disciplines. In this paper, we consider the zeroth-order setting where the…

In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…

In this paper, we present algorithms that perform gradient ascent of the average reward in a partially observable Markov decision process (POMDP). These algorithms are based on GPOMDP, an algorithm introduced in a companion paper (Baxter…

Motivated by decentralized sensing and policy evaluation problems, we consider a particular type of distributed stochastic optimization problem over a network, called the online stochastic distributed averaging problem. We design a…

Zeroth-order optimization aims to minimize an objective function using only function evaluations, and is therefore fundamental in black-box optimization, hyperparameter tuning, bandit learning, and adversarial machine learning. While…

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…

In spite of the accomplishments of deep learning based algorithms in numerous applications and very broad corresponding research interest, at the moment there is still no rigorous understanding of the reasons why such algorithms produce…

This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic…

Stochastic approximation algorithms are iterative procedures which are used to approximate a target value in an environment where the target is unknown and direct observations are corrupted by noise. These algorithms are useful, for…

The success of deep learning over the past decade mainly relies on gradient-based optimisation and backpropagation. This paper focuses on analysing the performance of first-order gradient-based optimisation algorithms, gradient descent and…

We address the problem of policy evaluation in discounted Markov decision processes, and provide instance-dependent guarantees on the $\ell_\infty$-error under a generative model. We establish both asymptotic and non-asymptotic versions of…

There are several applications of stochastic optimization where one can benefit from a robust estimate of the gradient. For example, domains such as distributed learning with corrupted nodes, the presence of large outliers in the training…

The conditional logit model is a standard workhorse approach to estimating customers' product feature preferences using choice data. Using these models at scale, however, can result in numerical imprecision and optimization failure due to a…

In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each…

Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…

Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…