Asymptotic normality of randomly truncated stochastic algorithms

TL;DR

This paper proves a central limit theorem for randomly truncated stochastic algorithms, like Robbins-Monro, ensuring their convergence rate under practical conditions, especially when the expected-value function grows rapidly.

Contribution

It provides a self-contained proof of asymptotic normality for truncated stochastic algorithms under easily verifiable local assumptions.

Findings

Establishes asymptotic normality of truncated Robbins-Monro algorithms.

Provides practical conditions for convergence rate analysis.

Enhances understanding of stochastic algorithms with truncation.

Abstract

We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function, which are fairly easy to check in practice.