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Main Authors: Jiang, Jiashuo, Ma, Will, Zhang, Jiawei
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2210.07996
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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