Online Inventory Optimization in Non-Stationary Environment

This paper addresses online inventory optimization (OIO), an extension of online convex optimization. OIO is a sequential decision-making process in inventory management cycles consisting of order arrival, stock consumption, and new order placement. One key challenge in OIO is managing demand fluctuations. However, most existing algorithms still cannot sufficiently handle this because they focus on a static regret guarantee, comparing their performance to a fixed order-up-to level strategy. In non-stationary environments, such static comparator is unsuitable due to demand fluctuations. In this paper, we propose an algorithm with near-optimal dynamic regret guarantee for OIO. Our algorithm also offers an improvement of $\sqrt{L_{\max}}$ for the static regret upper bound in existing studies. Here, $L_{\max}$ refers to the maximum sell-out period. Our algorithm employs a simple two-stage projection strategy, through which we prove that the OIO is connected to the smoothed online convex optimization.