Degeneracy is OK: Logarithmic Regret for Network Revenue Management with Indiscrete Distributions
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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 no further assumptions. We develop another online algorithm that achieves an improved O(log T) regret, with only a second-order growth assumption. To our knowledge, these are the first results achieving logarithmic-level regret in a continuous-distribution NRM model without further “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”.
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