A Note on KL-UCB+ Policy for the Stochastic Bandit
This is an incremental theoretical contribution for researchers in bandit algorithms, as it clarifies the regret bound for an existing policy without introducing new methods.
The paper tackles the problem of proving the asymptotic optimality of the KL-UCB+ policy in the stochastic K-armed bandit setting, showing that a simple proof can be derived using existing techniques, though no concrete numerical results are provided.
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.