Paper Overview
- Field: Machine Learning
- Authors: Anthony Pineci, Yunzong Xu
- Published: 2026-06-12
- arXiv: 2606.14679
- 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 a matching lower bound is proved.
- The same principle gives the first polylogarithmic regret guarantee for strongly convex losses.
- It provides the first dynamic regret guarantee adapting to Euclidean path variation on general convex capacity sets.
Summary
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.
The authors prove that this simple principle is optimal for OIO on arbitrary bounded convex capacity sets. Key results include:
Technical Insight
The analysis introduces a norm-alignment principle: the correct 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 as a scalar queue path, target movements act as arrivals, and common demand acts as service. This reduction to one-dimensional queue control resolves the state dependency and extends the guarantees to general convex capacity sets, beyond the reach of prior per-product approaches.
Experiments on synthetic and real-world inventory data confirm the theoretical results.
--- *Auto-collected on 2026-06-16. Source: arXiv:2606.14679*