Dynamic pricing under binary demand uncertainty: A multi-armed bandit with correlated arms

We consider a dynamic pricing problem with unknown demand models. In this problem, a seller offers prices sequentially to a stream of potential customers and observes either success or failure in each sales attempt. The underlying demand model is unknown and can take one of two possible forms. We show that the problem can be formulated as a two-armed bandit with correlated arms. We develop a dynamic pricing policy based on likelihood ratio test that offers a finite regret, where regret is defined as the revenue loss with respect to the case with a known demand model. We further generalize this policy by introducing an exploration price to improve the regret. The exploration price is set to be the one that maximizes the Kullback-Leibler divergence between the two demand models.