We study an off-policy contextual pricing problem where the seller has access to samples of prices that customers were previously offered, whether they purchased at that price, and auxiliary features describing the customer and/or item being sold. This is in contrast to the well-studied setting in which samples of the customer's valuation (willingness to pay) are observed. In our setting, the observed data is influenced by the previous pricing policy, and we do not know how customers would have responded to alternative prices. We introduce suitable loss functions for this setting that can be directly optimized to find an effective pricing policy with expected revenue guarantees, without the need for estimation of an intermediate demand function.
We focus on convex loss functions. This is particularly relevant when linear pricing policies are desired for interpretability reasons, resulting in a tractable convex revenue optimization problem. We propose generalized hinge and quantile pricing loss functions that price at a multiplicative factor of the conditional expected valuation or a particular quantile of the prices that sold, despite the valuation data not being observed. We prove expected revenue bounds for these pricing policies when the valuation distribution is log-concave, and we provide generalization bounds for the finite sample case. Finally, we conduct simulations on both synthetic and real-world data to demonstrate that this approach is competitive with, and in some settings outperforms, state-of-the-art methods in contextual pricing.
Bio: Max Biggs is an Assistant Professor of Business Administration at the University of Virginia, Darden School of Business. Max received his Ph.D. from the Operations Research Center at the Massachusetts Institute of Technology. Prior to joining Darden, Max was a Post-Doctoral Researcher at IBM Thomas J Watson Research Center. His research focuses on data-driven optimization and prescriptive analytics. Specifically, he is interested in using data, machine learning and optimization techniques to help solve operational decisions. Recent application areas include pricing and revenue management, healthcare, and logistics. Striving for research which is relevant to practice, he has collaborated with a range of companies including StubHub, Delta, IBM, Amazon and incasa - an on demand healthcare start-up.