Asymptotic normality of randomly truncated stochastic algorithms

TL;DR

This paper proves a central limit theorem for truncated stochastic algorithms, ensuring their convergence rate under practical conditions, which is useful when standard algorithms fail due to rapid growth of the expected-value function.

Contribution

It provides a self-contained proof of asymptotic normality for truncated Robbins-Monro algorithms under easy-to-verify local conditions.

Findings

Establishes asymptotic normality of truncated stochastic algorithms.

Provides practical conditions for convergence.

Enhances understanding of convergence rates in stochastic approximation.

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.