# Optimal Hidden-Target Learning for Online Inventory Optimization on General Convex Sets Source: [Optimal Hidden-Target Learning for Online Inventory Optimization on General Convex Sets]() Collection index: [llms.txt]() Data updated: 2026-06-16T05:00:14.254Z Authors: Anthony Pineci, Yunzong Xu Published: 2026-06-12T17:45:29.000Z ## Abstract Online inventory optimization (OIO) is online convex optimization with physical memory: inventory carryover makes the feasible action set depend on the past. A natural principle, used in stochastic inventory learning and recently in OIO under a single linear capacity constraint, is to maintain a hidden target chosen by an online learner and implement its projection onto the currently feasible order-up-to set. We prove that this simple principle is optimal for OIO on arbitrary bounded convex capacity sets. With online gradient descent as the base learner, the method improves the best known regret guarantee for OIO on general convex sets from inverse to inverse-square-root dependence on the common-demand probability, and we prove a matching lower bound. The same principle gives the first polylogarithmic regret guarantee for strongly convex losses and the first dynamic regret guarantee adapting to Euclidean path variation on general convex capacity sets. The analysis introduces a norm alignment principle: the right state variable is the distance from the hidden target to the feasible set, measured in the same norm as the projection. Under norm alignment, this distance evolves pathwise as a scalar queue, with target movement as arrival and common demand as service. This reduction to one-dimensional queue control resolves the state dependence and extends the guarantees to general convex capacity sets, beyond the reach of prior productwise approaches. Experiments on synthetic and real-world inventory data corroborate the theory. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Online Inventory Optimization on Adversarial-demand Online Inventory Optimization Dynamic](): Online Inventory Optimization; Adversarial-demand Online Inventory Optimization Dynamic; Upper Bound: 1. - [Online Inventory Optimization on Adversarial Demand Static Setting](): Online Inventory Optimization; Adversarial-demand Online Inventory Optimization Static; Upper Bound: not recorded. ## Original sources and implementation [Original paper]() [PDF]()