Best Arm Identification for Stochastic Rising Bandits

Stochastic Rising Bandits is a setting in which the values of the expected rewards of the available options increase every time they are selected. This framework models a wide range of scenarios in which the available options are learning entities whose performance improves over time. In this paper, we focus on the Best Arm Identification (BAI) problem for the stochastic rested rising bandits. In this scenario, we are asked, given a fixed budget of rounds, to provide a recommendation about the best option at the end of the selection process. We propose two algorithms to tackle the above-mentioned setting, namely R-UCBE, which resorts to a UCB-like approach, and R-SR, which employs a successive reject procedure. We show that they provide guarantees on the probability of properly identifying the optimal option at the end of the learning process. Finally, we numerically validate the proposed algorithms in synthetic and realistic environments and compare them with the currently available BAI strategies.