  Supply chain management (SCM) has been recognized as an important discipline
with applications to many industries, where the two-echelon stochastic
inventory model, involving one downstream retailer and one upstream supplier,
plays a fundamental role for developing firms' SCM strategies. In this work, we
aim at designing online learning algorithms for this problem with an unknown
demand distribution, which brings distinct features as compared to classic
online optimization problems. Specifically, we consider the two-echelon supply
chain model introduced in [Cachon and Zipkin, 1999] under two different
settings: the centralized setting, where a planner decides both agents'
strategy simultaneously, and the decentralized setting, where two agents decide
their strategy independently and selfishly. We design algorithms that achieve
favorable guarantees for both regret and convergence to the optimal inventory
decision in both settings, and additionally for individual regret in the
decentralized setting. Our algorithms are based on Online Gradient Descent and
Online Newton Step, together with several new ingredients specifically designed
for our problem. We also implement our algorithms and show their empirical
effectiveness.
