Learning with Posterior Sampling for Revenue Management under Time-varying Demand

TL;DR

This paper introduces a posterior sampling algorithm for revenue management with time-varying, unknown demand, demonstrating improved performance over benchmarks and near-optimal results through empirical evaluation.

Contribution

It develops a computationally efficient posterior sampling method for dynamic pricing under unknown, time-varying demand, with theoretical regret bounds and empirical validation.

Findings

The algorithm outperforms benchmark methods in experiments.

It achieves near-optimal revenue compared to the hindsight optimal.

The heuristic modification enhances learning efficiency.

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.