A Minibatch-SGD-based Learning Meta-Policy for Inventory Systems with Myopic Optimal Policy

Stochastic gradient descent (SGD) has proven effective in solving many inventory control problems with demand learning. However, it often faces the pitfall of an infeasible target inventory level that is lower than the current inventory level. Several recent works (e.g., (Huh and Rusmevichientong 2009, Shi et al. 2016)) are successful to resolve this issue in various inventory systems. However, their techniques are rather sophisticated and difficult to be applied to more complicated scenarios such as multi-product and multi-constraint inventory systems. In this paper, we address the infeasible-target-inventory-level issue from a new technical perspective -- we propose a novel minibatch-SGD-based meta-policy. Our meta-policy is flexible enough to be applied to a general inventory systems framework covering a wide range of inventory management problems with myopic clairvoyant optimal policy. By devising the optimal mini-batch scheme, our meta-policy achieves O(T^(1/2)) regret for the general convex case and O(log T) regret for the strongly convex case. To demonstrate the power and flexibility of our meta-policy, we apply it to three important inventory control problems: multi-product and multi-constraint systems, multi-echelon serial systems, and one-warehouse and multi-store systems by carefully designing application-specific subroutines. Numerical experiments on the multi-product multi-constraint systems show that our algorithm has low average costs and high computational efficiency