Learning to Price Against a Moving Target

TL;DR

This paper investigates dynamic pricing strategies where the buyer's valuation changes over time, providing bounds on revenue loss and highlighting the challenges of balancing exploration and exploitation in non-stationary environments.

Contribution

It introduces the first theoretical bounds for pricing against a moving target, addressing both stochastic and adversarial valuation changes.

Findings

Established upper and lower bounds on revenue loss in non-stationary settings

Demonstrated the necessity of frequent exploration-exploitation switching

Provided insights into algorithm design for dynamic pricing with evolving buyer valuations

Abstract

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.