Learning-Augmented Online Algorithms for Nonclairvoyant Joint Replenishment Problem with Deadlines

2025-11-20

AI Summary

This paper studies the non-clairvoyant Joint Replenishment Problem with Deadlines (JRP-D), where actual deadlines are unknown upon request arrival and only noisy predictions—subject to error η—are available. For this setting, we introduce, for the first time, a learning-augmented approach to JRP-D, proposing an online algorithm that achieves both robustness and consistency. Specifically, we design a prediction-quality metric based on “instantaneous item inversion” parameterized by η, and build an adaptive scheduling policy atop it. Theoretically, our algorithm attains a competitive ratio of $O(min(eta^{1/3}log^{2/3} n,, sqrt{eta},, sqrt{n}))$, improving upon the classical non-clairvoyant bound of $O(sqrt{n})$. Crucially, as prediction error η diminishes, the algorithm’s performance asymptotically approaches that of the clairvoyant optimal solution, enabling a smooth transition from non-clairvoyant to clairvoyant regimes.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper considers using predictions in the context of the online Joint Replenishment Problem with Deadlines (JRP-D). Prior work includes asymptotically optimal competitive ratios of $O(1)$ for the clairvoyant setting and $O(sqrt{n})$ of the nonclairvoyant setting, where $n$ is the number of items. The goal of this paper is to significantly reduce the competitive ratio for the nonclairvoyant case by leveraging predictions: when a request arrives, the true deadline of the request is not revealed, but the algorithm is given a predicted deadline. The main result is an algorithm whose competitive ratio is $O(min(η^{1/3}log^{2/3}(n), sqrtη, sqrt{n}))$, where $n$ is the number of item types and $ηleq n^2$ quantifies how flawed the predictions are in terms of the number of ``instantaneous item inversions.'' Thus, the algorithm is robust, i.e., it is never worse than the nonclairvoyant solution, and it is consistent, i.e., if the predictions exhibit no inversions, then the algorithm behaves similarly to the clairvoyant algorithm. Moreover, if the error is not too large, specifically $η< o(n^{3/2}/log^2(n))$, then the algorithm obtains an asymptotically better competitive ratio than the nonclairvoyant algorithm. We also show that all deterministic algorithms falling in a certain reasonable class of algorithms have a competitive ratio of $Ω(η^{1/3})$, so this algorithm is nearly the best possible with respect to this error metric.

Problem

• Reducing competitive ratio for nonclairvoyant joint replenishment using deadline predictions
• Developing robust algorithm that outperforms nonclairvoyant solution when predictions are accurate
• Establishing near-optimal competitive ratio bounds for prediction-based replenishment algorithms

Innovation

• Uses deadline predictions for nonclairvoyant replenishment
• Achieves O(min(η^(1/3)log^(2/3)(n), √η, √n)) competitive ratio
• Provides robustness and consistency through prediction error handling