# A Note on KL-UCB+ Policy for the Stochastic Bandit

arXiv: https://arxiv.org/abs/1903.07839 · HTML: https://mlsanity.com/paper/1903.07839/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2019.

## Built on by (most cited first, 4 of 4)

- [Variational Bayesian Optimistic Sampling](https://mlsanity.com/paper/2110.15688/) (2021)
- [On Lai's Upper Confidence Bound in Multi-Armed Bandits](https://mlsanity.com/paper/2410.02279/) (2024)
- [Blind Exploration and Exploitation of Stochastic Experts](https://mlsanity.com/paper/2104.01078/) (2021)
- [Optimal Regret of Bernoulli Bandits under Global Differential Privacy](https://mlsanity.com/paper/2505.05613/) (2025)

## Abstract (arXiv)

A classic setting of the stochastic K-armed bandit problem is considered in this note. In this problem it has been known that KL-UCB policy achieves the asymptotically optimal regret bound and KL-UCB+ policy empirically performs better than the KL-UCB policy although the regret bound for the original form of the KL-UCB+ policy has been unknown. This note demonstrates that a simple proof of the asymptotic optimality of the KL-UCB+ policy can be given by the same technique as those used for analyses of other known policies.