An ε-Best-Arm Identification Algorithm for Fixed-Confidence and Beyond
Abstract
We propose EB-TCε, a novel sampling rule for ε-best arm identification in stochastic bandits. It is the first instance of Top Two algorithm analyzed for approximate best arm identification. EB-TCε is an anytime sampling rule that can therefore be employed without modification for fixed confidence or fixed budget identification (without prior knowledge of the budget). We provide three types of theoretical guarantees for EB-TCε. First, we prove bounds on its expected sample complexity in the fixed confidence setting, notably showing its asymptotic optimality in combination with an adaptive tuning of its exploration parameter. We complement these findings with upper bounds on its probability of error at any time and for any error parameter, which further yield upper bounds on its simple regret at any time. Finally, we show through numerical simulations that EB-TCε performs favorably compared to existing algorithms, in different settings.
Marc Jourdan
PhD Student
PhD student at Scool (Inria), I study identification problems in Multi-Armed Bandits.
Rémy Degenne
INRIA researcher
