  We consider a personalized pricing problem in which we have data consisting
of feature information, historical pricing decisions, and binary realized
demand. The goal is to perform off-policy evaluation for a new personalized
pricing policy that maps features to prices. Methods based on inverse
propensity weighting (including doubly robust methods) for off-policy
evaluation may perform poorly when the logging policy has little exploration or
is deterministic, which is common in pricing applications. Building on the
balanced policy evaluation framework of Kallus (2018), we propose a new
approach tailored to pricing applications. The key idea is to compute an
estimate that minimizes the worst-case mean squared error or maximizes a
worst-case lower bound on policy performance, where in both cases the
worst-case is taken with respect to a set of possible revenue functions. We
establish theoretical convergence guarantees and empirically demonstrate the
advantage of our approach using a real-world pricing dataset.
