Learning with Posterior Sampling for Revenue Management under Time-varying Demand
Kazuma Shimizu, Junya Honda, Shinji Ito, Shinji Nakadai
TL;DR
The paper tackles revenue management under time-varying, unknown demand by introducing an episodic RM framework with limited inventory. It develops two LP-based Thompson sampling algorithms, TS-episodic and TS-dynamic, to balance exploration and exploitation across episodes while accounting for inventory constraints. The authors prove Bayesian regret upper and lower bounds, showing sublinear performance in the number of sales periods, and demonstrate empirically that the proposed methods approach the hindsight-optimal policy, with TS-dynamic notably accelerating learning. The approach is flexible, accommodating Poisson-Gamma priors and Gaussian-process priors to capture temporal correlations, and offers practical, scalable pricing strategies for real-world RM problems.
Abstract
This paper discusses the revenue management (RM) problem to maximize revenue by pricing items or services. One challenge in this problem is that the demand distribution is unknown and varies over time in real applications such as airline and retail industries. In particular, the time-varying demand has not been well studied under scenarios of unknown demand due to the difficulty of jointly managing the remaining inventory and estimating the demand. To tackle this challenge, we first introduce an episodic generalization of the RM problem motivated by typical application scenarios. We then propose a computationally efficient algorithm based on posterior sampling, which effectively optimizes prices by solving linear programming. We derive a Bayesian regret upper bound of this algorithm for general models where demand parameters can be correlated between time periods, while also deriving a regret lower bound for generic algorithms. Our empirical study shows that the proposed algorithm performs better than other benchmark algorithms and comparably to the optimal policy in hindsight. We also propose a heuristic modification of the proposed algorithm, which further efficiently learns the pricing policy in the experiments.