Informational Confidence Bounds for Self-Normalized Averages and Applications

TL;DR

This paper introduces deviation bounds for self-normalized averages using exponential martingale techniques, with applications in bandit problems and context tree estimation, providing a novel approach to estimation with random sample sizes.

Contribution

It presents an alternative to the mixture method for deriving deviation bounds, specifically tailored for self-normalized averages in stochastic estimation problems.

Findings

Provides new deviation bounds for self-normalized averages.

Demonstrates applications in bandit problems and context tree estimation.

Offers an alternative to existing methods like the mixture approach.

Abstract

We present deviation bounds for self-normalized averages and applications to estimation with a random number of observations. The results rely on a peeling argument in exponential martingale techniques that represents an alternative to the method of mixture. The motivating examples of bandit problems and context tree estimation are detailed.