Against the Odds: Achieving Low Regret in Network Revenue Management with Indiscrete and Degenerate Distributions

Abstract

This paper explores the problem of regret minimization in Network Revenue Management (NRM) under the rarely examined but practically relevant settings where demand distributions are either indiscrete (i.e., continuous but not smoothly distributed) or degenerate (i.e., having mass concentrated at specific points). Traditional NRM algorithms rely on assumptions such as demand smoothness and discretization to provide performance guarantees. We challenge these assumptions and develop a robust learning framework that adapts to discontinuities and concentrated demand masses. Our approach leverages distribution-agnostic techniques and adaptive thresholds to achieve low regret over time. We demonstrate, both theoretically and through simulations,that our model maintains performance guarantees even in worst-case demand configurations, thereby extending the applicability of NRM methods in real-world logistics and pricing systems.