# The KL-UCB Algorithm for Bounded Stochastic Bandits and Beyond

@inproceedings{Garivier2011TheKA, title={The KL-UCB Algorithm for Bounded Stochastic Bandits and Beyond}, author={Aur{\'e}lien Garivier and Olivier Capp{\'e}}, booktitle={Annual Conference Computational Learning Theory}, year={2011} }

This paper presents a finite-time analysis of the KL-UCB algorithm, an online, horizon-free index policy for stochastic bandit problems. We prove two distinct results: first, for arbitrary bounded rewards, the KL-UCB algorithm satisfies a uniformly better regret bound than UCB or UCB2; second, in the special case of Bernoulli rewards, it reaches the lower bound of Lai and Robbins. Furthermore, we show that simple adaptations of the KL-UCB algorithm are also optimal for specific classes of…

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