Degeneracy is OK: Logarithmic Regret for Network Revenue Management with Indiscrete Distributions
This provides logarithmic regret guarantees for revenue management in online settings, addressing a long-standing challenge with continuous distributions, though it is incremental in extending prior discrete results.
The paper tackles the Network Revenue Management problem with continuous random values and achieves O(log^2 T) regret under minimal assumptions, improving to O(log T) with additional growth conditions, without requiring non-degeneracy assumptions.
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".