The prevalence of ecommerce has made customers’ detailed personal information readily accessible to retailers, and this information has been widely used in pricing decisions. When using personalized information, the question of how to protect the privacy of such information becomes a critical issue in practice. In this paper, we consider a dynamic pricing problem over T time periods with an unknown demand function of posted price and personalized information. At each time t, the retailer observes an arriving customer’s personal information and offers a price. The customer then makes the purchase decision, which will be utilized by the retailer to learn the underlying demand function. There is potentially a serious privacy concern during this process: a thirdparty agent might infer the personalized information and purchase decisions from price changes in the pricing system. Using the fundamental framework of differential privacy from computer science, we develop a privacypreserving dynamic pricing policy, which tries to maximize the retailer revenue while avoiding information leakage of individual customer’s information and purchasing decisions. To this end, we first introduce a notion of anticipating [Formula: see text]differential privacy that is tailored to the dynamic pricing problem. Our policy achieves both the privacy guarantee and the performancemore »
This content will become publicly available on April 1, 2023
Robust Dynamic Pricing with Demand Learning in the Presence of Outlier Customers
This paper studies a dynamic pricing problem under model misspecification. To characterize model misspecification, we adopt the εcontamination model—the most fundamental model in robust statistics and machine learning. In particular, for a selling horizon of length T, the online εcontamination model assumes that demands are realized according to a typical unknown demand function only for [Formula: see text] periods. For the rest of [Formula: see text] periods, an outlier purchase can happen with arbitrary demand functions. The challenges brought by the presence of outlier customers are mainly due to the fact that arrivals of outliers and their exhibited demand behaviors are completely arbitrary, therefore calling for robust estimation and exploration strategies that can handle any outlier arrival and demand patterns. We first consider unconstrained dynamic pricing without any inventory constraint. In this case, we adopt the FollowtheRegularizedLeader algorithm to hedge against outlier purchase behavior. Then, we introduce inventory constraints. When the inventory is insufficient, we study a robust bisectionsearch algorithm to identify the clearance price—that is, the price at which the initial inventory is expected to clear at the end of T periods. Finally, we study the general dynamic pricing case, where a retailer has no clue whether the inventory more »
 Award ID(s):
 1845444
 Publication Date:
 NSFPAR ID:
 10376124
 Journal Name:
 Operations Research
 ISSN:
 0030364X
 Sponsoring Org:
 National Science Foundation
More Like this


We consider the periodic review dynamic pricing and inventory control problem with fixed ordering cost. Demand is random and price dependent, and unsatisfied demand is backlogged. With complete demand information, the celebrated [Formula: see text] policy is proved to be optimal, where s and S are the reorder point and orderupto level for ordering strategy, and [Formula: see text], a function of onhand inventory level, characterizes the pricing strategy. In this paper, we consider incomplete demand information and develop online learning algorithms whose average profit approaches that of the optimal [Formula: see text] with a tight [Formula: see text] regret rate. A number of salient features differentiate our work from the existing online learning researches in the operations management (OM) literature. First, computing the optimal [Formula: see text] policy requires solving a dynamic programming (DP) over multiple periods involving unknown quantities, which is different from the majority of learning problems in OM that only require solving singleperiod optimization questions. It is hence challenging to establish stability results through DP recursions, which we accomplish by proving uniform convergence of the profittogo function. The necessity of analyzing actiondependent state transition over multiple periods resembles the reinforcement learning question, considerably more difficult thanmore »

Pricebased revenue management is an important problem in operations management with many practical applications. The problem considers a seller who sells one or multiple products over T consecutive periods and is subject to constraints on the initial inventory levels of resources. Whereas, in theory, the optimal pricing policy could be obtained via dynamic programming, computing the exact dynamic programming solution is often intractable. Approximate policies, such as the resolving heuristics, are often applied as computationally tractable alternatives. In this paper, we show the following two results for pricebased network revenue management under a continuous price set. First, we prove that a natural resolving heuristic attains O(1) regret compared with the value of the optimal policy. This improves the [Formula: see text] regret upper bound established in the prior work by Jasin in 2014. Second, we prove that there is an [Formula: see text] gap between the value of the optimal policy and that of the fluid model. This complements our upper bound result by showing that the fluid is not an adequate informationrelaxed benchmark when analyzing pricebased revenue management algorithms. Funding: This work was supported in part by the National Science Foundation [Grant CMMI2145661].

In recent decades, the advance of information technology and abundant personal data facilitate the application of algorithmic personalized pricing. However, this leads to the growing concern of potential violation of privacy because of adversarial attack. To address the privacy issue, this paper studies a dynamic personalized pricing problem with unknown nonparametric demand models under data privacy protection. Two concepts of data privacy, which have been widely applied in practices, are introduced: central differential privacy (CDP) and local differential privacy (LDP), which is proved to be stronger than CDP in many cases. We develop two algorithms that make pricing decisions and learn the unknown demand on the fly while satisfying the CDP and LDP guarantee, respectively. In particular, for the algorithm with CDP guarantee, the regret is proved to be at most [Formula: see text]. Here, the parameter T denotes the length of the time horizon, d is the dimension of the personalized information vector, and the key parameter [Formula: see text] measures the strength of privacy (smaller ε indicates a stronger privacy protection). Conversely, for the algorithm with LDP guarantee, its regret is proved to be at most [Formula: see text], which is near optimal as we prove a lowermore »

We study the dynamic assortment planning problem, where for each arriving customer, the seller offers an assortment of substitutable products and the customer makes the purchase among offered products according to an uncapacitated multinomial logit (MNL) model. Because all the utility parameters of the MNL model are unknown, the seller needs to simultaneously learn customers’ choice behavior and make dynamic decisions on assortments based on the current knowledge. The goal of the seller is to maximize the expected revenue, or, equivalently, to minimize the expected regret. Although dynamic assortment planning problem has received an increasing attention in revenue management, most existing policies require the estimation of mean utility for each product and the final regret usually involves the number of products [Formula: see text]. The optimal regret of the dynamic assortment planning problem under the most basic and popular choice model—the MNL model—is still open. By carefully analyzing a revenue potential function, we develop a trisectionbased policy combined with adaptive confidence bound construction, which achieves an itemindependent regret bound of [Formula: see text], where [Formula: see text] is the length of selling horizon. We further establish the matching lower bound result to show the optimality of our policy. There aremore »