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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 order-up-to level for ordering strategy, and [Formula: see text], a function of on-hand 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 single-period optimization questions. It is hence challenging to establish stability results through DP recursions, which we accomplish by proving uniform convergence of the profit-to-go function. The necessity of analyzing action-dependent state transition over multiple periods resembles the reinforcement learning question, considerably more difficult than existing bandit learning algorithms. Second, the pricing function [Formula: see text] is of infinite dimension, and approaching it is much more challenging than approaching a finite number of parameters as seen in existing researches. The demand-price relationship is estimated based on upper confidence bound, but the confidence interval cannot be explicitly calculated due to the complexity of the DP recursion. Finally, because of the multiperiod nature of [Formula: see text] policies the actual distribution of the randomness in demand plays an important role in determining the optimal pricing strategy [Formula: see text], which is unknown to the learner a priori. In this paper, the demand randomness is approximated by an empirical distribution constructed using dependent samples, and a novel Wasserstein metric-based argument is employed to prove convergence of the empirical distribution. This paper was accepted by J. George Shanthikumar, big data analytics. 

The prevalence of e-commerce 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 third-party 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 privacy-preserving 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 performance guarantee in terms of regret. Roughly speaking, for d-dimensional personalized information, our algorithm achieves the expected regret at the order of [Formula: see text] when the customers’ information is adversarially chosen. For stochastic personalized information, the regret bound can be further improved to [Formula: see text]. This paper was accepted by J. George Shanthikumar, big data analytics. 

We consider a logit model-based framework for modeling joint pricing and assortment decisions that take into account customer features. This model provides a significant advantage when one has insufficient data for any one customer and wishes to generalize learning about one customer’s preferences to the population. Under this model, we study the statistical learning task of model fitting from a static store of precollected customer data. This setting, in contrast to the popular learning and earning paradigm, represents the situation many business teams encounter in which their data collection abilities have outstripped their data analysis capabilities. In this learning setting, we establish finite-sample convergence guarantees on the model parameters. The parameter convergence guarantees are then extended to out-of-sample performance guarantees in terms of revenue, in the form of a high-probability bound on the gap between the expected revenue of the best action taken under the estimated parameters and the revenue generated by a decision maker with full knowledge of the choice model. We further discuss practical implications of these bounds. We demonstrate the personalization approach using ticket purchase data from an airline carrier. This paper was accepted by J. George Shanthikumar, special issue on data-driven prescriptive analytics