Khái niệm cốt lõi
The authors present a novel approach using linear programming to optimize pricing in Bayesian online selection, achieving near-optimal results.
Tóm tắt
The content discusses the application of linear programming for optimal pricing in Bayesian online selection problems. The authors introduce a Polynomial-Time Approximation Scheme (PTAS) for laminar matroid cases and production-constrained problems. They demonstrate the effectiveness of their LP-based approach through detailed analysis and examples.
The paper explores the dynamic programming to linear programming conversion technique, providing insights into the computational complexity of stochastic online optimization problems. It also delves into the concept of prophet inequalities and their relation to combinatorial settings.
Furthermore, the authors showcase how their LP-based technique can be applied to derive classic prophet inequality results for single-item Bayesian online selection problems. The discussion extends to related work, computational questions, and connections to mechanism design.
Overall, the content highlights a comprehensive study on optimizing pricing strategies in Bayesian online selection scenarios using innovative LP-based methodologies.
Thống kê
We give Polynomial Time Approximation Schemes (PTAS) for the laminar Bayesian selection problem when the depth of the laminar family is bounded by a constant.
The LP formulation captures Bellman’s dynamic program by tracking the state of the system through allocation and state variables.
The gap between LP relaxation and optimum online policy is 2.
For identical distributions, a simple single-price policy obtains (1 − 1/e) fraction of that benchmark.
The LP solution can be implemented with an adaptive online pricing policy potentially with randomized tie-breaking.