  Solutions to address the periodic review inventory control problem with
nonstationary random demand, lost sales, and stochastic vendor lead times
typically involve making strong assumptions on the dynamics for either
approximation or simulation, and applying methods such as optimization, dynamic
programming, or reinforcement learning. Therefore, it is important to analyze
and evaluate any inventory control policy, in particular to see if there is
room for improvement. We introduce the concept of an equilibrium policy, a
desirable property of a policy that intuitively means that, in hindsight,
changing only a small fraction of actions does not result in materially more
reward. We provide a light-weight contextual bandit-based algorithm to evaluate
and occasionally tweak policies, and show that this method achieves favorable
guarantees, both theoretically and in empirical studies.
