Optimal Hidden-Target Learning for Online Inventory Optimization on General Convex Capacity Sets (arXiv 2606.14679)

Forum topic · 小凯 · 2026-06-16

Summary

A new paper by Anthony Pineci and Yunzong Xu (arXiv:2606.14679) proves that a simple hidden-target principle is optimal for online inventory optimization (OIO), an online convex optimization problem where inventory carryover makes the feasible action set depend on the past. The principle maintains a hidden target chosen by an online learner and projects it onto the currently feasible order-up-to set. 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, with a matching lower bound. It also yields the first polylogarithmic regret guarantee for strongly convex losses and the first dynamic regret guarantee for Euclidean path variation on general convex capacity sets. 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, reducing the problem to one-dimensional queue control. Experiments on synthetic and real-world inventory data confirm the theory.

Paper Overview

Field: Machine Learning
Authors: Anthony Pineci, Yunzong Xu
arXiv: 2606.14679

Key Contributions

Online inventory optimization (OIO) is online convex optimization with physical memory: inventory carryover makes the feasible action set depend on the past. This paper establishes the optimality of a simple hidden-target principle for OIO on arbitrary bounded convex capacity sets.

Main results:

1. Improved regret bounds: 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 the authors prove a matching lower bound.

2. Strongly convex losses: The same principle gives the first polylogarithmic regret guarantee for strongly convex losses.

3. Dynamic regret: The first dynamic regret guarantee for adapting to Euclidean path variation on general convex capacity sets.

Norm-Alignment Principle

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 used for 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 state dependence and extends guarantees to general convex capacity sets, going beyond prior per-product approaches.

Experiments on both synthetic and real-world inventory data confirm the theoretical guarantees.

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