Dynamic Pricing with Demand Covariates

We consider a firm that sells a product over T periods without knowing the demand function. The firm sequentially sets prices to earn revenue and to learn the underlying demand function simultaneously. In practice, this problem is commonly solved via greedy iterative least squares (GILS). At each time period, GILS estimates the demand as a linear function of the price by applying least squares to the set of prior prices and realized demands. Then a price that maximizes the revenue is used for the next period. The performance is measured by the regret, which is the expected revenue compared to an oracle that knows the true demand function. Recently, den Boer and Zwart (2014), Keskin and Zeevi (2014) demonstrated that GILS is sub-optimal and introduced optimal algorithms which integrate forced price-dispersion with GILS. Here, we consider this dynamic pricing problem in a data-rich environment. We assume that the firm has access to demand covariates which may be predictive of the demand and prove that GILS achieves an asymptotically optimal regret of order log(T ). We also show that the asymptotic optimality of GILS holds even when the covariates are uninformative. We validate our results via simulations on synthetic and real data.