Regular Article: Optimal Adaptive Policies for Sequential Allocation Problems
Advances in Applied Mathematics
Journal of the ACM (JACM)
The Nonstochastic Multiarmed Bandit Problem
SIAM Journal on Computing
Finite-time Analysis of the Multiarmed Bandit Problem
Machine Learning
Prediction, Learning, and Games
Prediction, Learning, and Games
Multi-armed bandits in metric spaces
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Exploration-exploitation tradeoff using variance estimates in multi-armed bandits
Theoretical Computer Science
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This paper is devoted to regret lower bounds in the classical model of stochastic multi-armed bandit. A well-known result of Lai and Robbins, which has then been extended by Burnetas and Katehakis, has established the presence of a logarithmic bound for all consistent policies. We relax the notion of consistency, and exhibit a generalisation of the bound. We also study the existence of logarithmic bounds in general and in the case of Hannan consistency. Moreover, we prove that it is impossible to design an adaptive policy that would select the best of two algorithms by taking advantage of the properties of the environment. To get these results, we study variants of popular Upper Confidence Bounds (UCB) policies.