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Differentially Private Contextual Dynamic Pricing

In this paper, we design differentially private algorithms for the contextual dynamic pricing problem. In contextual dynamic pricing, the seller sells heterogeneous products to buyers that arrive sequentially. At each time step, a buyer arrives with interests in purchasing a product. Each product is represented by a set of product features, i.e., the context, and the buyer’s valuation for the product is a function of the product features and the buyer’s private preferences. The goal of contextual dynamic pricing is to adjust the price over time to learn how to set the optimal price for the population from interacting with individual buyers. In the meantime, this learning process creates potential privacy concerns for individual buyers. A third-party agent might be able to infer the information of individual buyers from how the prices change after the participation of a particular buyer. In this work, using the notion of differential privacy as our privacy measure, we explore the design of differentially private dynamic pricing algorithms. The goal is to maximize the seller’s payoff, or equivalently, minimize the regret with respect to the optimal policy when knowing the distribution of buyers’ preferences while ensuring the amount of privacy leak of individual buyers’ valuations is bounded. We present an algorithm that is ε-differentially private and achieves expected regret Õ (√dT ε ) , where d is the dimension of product features andT is the time horizon.