Degeneracy is OK: Logarithmic Regret for Network Revenue Management with Indiscrete Distributions

2022-10-14

arXiv.org

AI Summary

This paper studies the online decision-making problem in network revenue management (NRM) under continuous value distributions, focusing on a joint arrival model where resource consumption types are finite and rewards arrive stochastically within bounded intervals; the objective is to minimize regret on a logarithmic scale. We propose a novel online algorithm that dispenses with the non-degeneracy assumption, built upon three key components: a semi-fluid relaxation framework, single-step regret analysis, and an enhanced dual convergence technique. Our work establishes the first $O(log^2 T)$ regret bound for general continuous-value NRM, and under a second-order growth condition on the dual function, further improves it to $O(log T)$. Crucially, this is the first result to remove reliance on non-degeneracy assumptions—previously required in all existing continuous-value NRM analyses—thereby substantially broadening the theoretical applicability of regret-optimal algorithms in stochastic online resource allocation.

Abstract

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".

Problem

• Online Algorithm
• Network Revenue Management
• Logarithmic Regret

Innovation

• Online Algorithm
• Logarithmic Regret
• Resource Allocation Optimization