Dynamic Learning and Pricing with Model Misspecification

We study a multi-period dynamic pricing problem with contextual information where the seller uses a misspecified demand model. The seller sequentially observes past demand, updates model parameters, and then chooses the price for the next period based on time-varying features. We show that model misspecification leads to correlation between price and prediction error of demand per period, which in turn leads to inconsistent price elasticity estimate and hence suboptimal pricing decisions. We propose a “random price shock” (RPS) algorithm that dynamically generates randomized price shocks to estimate price elasticity while maximizing revenue. We show that the RPS algorithm has strong theoretical performance guarantees, that it is robust to model misspecification, and that it can be adapted to a number of business settings, including (1) when the feasible price set is a price ladder, and (2) when the contextual information is not IID. We also perform offline simulations gauging the performance of RPS on a large fashion retail dataset, and find that is expected to earn 8~20% more revenue on average than competing algorithms that do not account for price endogeneity.