Learning to Price Against a Moving Target
This addresses a practical challenge for sellers in non-stationary markets, though it is incremental as it extends well-understood stationary pricing models.
The paper tackles the problem of dynamic pricing when buyer valuations change over time, either stochastically or adversarially, and provides matching upper and lower bounds on the optimal revenue loss.
In the Learning to Price setting, a seller posts prices over time with the goal of maximizing revenue while learning the buyer's valuation. This problem is very well understood when values are stationary (fixed or iid). Here we study the problem where the buyer's value is a moving target, i.e., they change over time either by a stochastic process or adversarially with bounded variation. In either case, we provide matching upper and lower bounds on the optimal revenue loss. Since the target is moving, any information learned soon becomes out-dated, which forces the algorithms to keep switching between exploring and exploiting phases.