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Dynamic Pricing under Finite Space Demand Uncertainty: A Multi-Armed Bandit with Correlated Arms

Abstract

We consider a dynamic pricing problem under unknown demand models. In this problem a seller offers prices to a stream of customers and observes either success or failure in each sale attempt. The underlying demand model is unknown to the seller and can take one of NN possible forms. In this paper, we show that this problem can be formulated as a multi-armed bandit with dependent arms. We propose a dynamic pricing policy based on the likelihood ratio test. We show that the proposed policy achieves complete learning, i.e., it offers a bounded regret where regret is defined as the revenue loss with respect to the case with a known demand model. This is in sharp contrast with the logarithmic growing regret in multi-armed bandit with independent arms.

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