Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.07996 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910769818370048 |
|---|---|
| author | Jiang, Jiashuo Ma, Will Zhang, Jiawei |
| author_facet | Jiang, Jiashuo Ma, Will Zhang, Jiawei |
| contents | We study the classical Network Revenue Management (NRM) problem with accept/reject decisions and $T$ IID arrivals. We consider a distributional form where each arrival must fall under a finite number of possible categories, each with a deterministic resource consumption vector, but a random value distributed continuously over an interval. We develop an online algorithm that achieves $O(\log^2 T)$ regret under this model, with the only (necessary) assumption being that the probability densities are bounded away from 0. We derive a second result that achieves $O(\log T)$ regret under an additional assumption of second-order growth. To our knowledge, these are the first results achieving logarithmic-level regret in an NRM model with continuous values that do not require any kind of "non-degeneracy" assumptions. Our results are achieved via new techniques including a new method of bounding myopic regret, a "semi-fluid" relaxation of the offline allocation, and an improved bound on the "dual convergence". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07996 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Degeneracy is OK: Logarithmic Regret for Network Revenue Management with Indiscrete Distributions Jiang, Jiashuo Ma, Will Zhang, Jiawei Machine Learning Probability We study the classical Network Revenue Management (NRM) problem with accept/reject decisions and $T$ IID arrivals. We consider a distributional form where each arrival must fall under a finite number of possible categories, each with a deterministic resource consumption vector, but a random value distributed continuously over an interval. We develop an online algorithm that achieves $O(\log^2 T)$ regret under this model, with the only (necessary) assumption being that the probability densities are bounded away from 0. We derive a second result that achieves $O(\log T)$ regret under an additional assumption of second-order growth. To our knowledge, these are the first results achieving logarithmic-level regret in an NRM model with continuous values that do not require any kind of "non-degeneracy" assumptions. Our results are achieved via new techniques including a new method of bounding myopic regret, a "semi-fluid" relaxation of the offline allocation, and an improved bound on the "dual convergence". |
| title | Degeneracy is OK: Logarithmic Regret for Network Revenue Management with Indiscrete Distributions |
| topic | Machine Learning Probability |
| url | https://arxiv.org/abs/2210.07996 |