Informational confidence bounds for self-normalized averages and applications

Aurélien Garivier

74 citations0/0 files storedIEEE Information Theory Workshop (ITW)

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Advanced Bandit Algorithms Research Probability and Statistical Research Statistical Methods and Inference

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.

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References

2002Finite-time Analysis of the Multiarmed Bandit Problem 2012Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems 2012Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems 2011Improved Algorithms for Linear Stochastic Bandits 2009Exploration–exploitation tradeoff using variance estimates in multi-armed bandits 1995Sample mean based index policies byO(logn) regret for the multi-armed bandit problem 2011On Upper-Confidence Bound Policies for Switching Bandit Problems 2011The KL-UCB Algorithm for Bounded Stochastic Bandits and Beyond

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2015Regret Analysis of the Finite-Horizon Gittins Index Strategy for Multi-Armed Bandits 2016Conservative Bandits

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