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

TL;DR

This paper introduces a learning-augmented online algorithm for the nonclairvoyant joint replenishment problem with deadlines, significantly improving competitive ratios by leveraging predictions about request deadlines.

Contribution

It presents a robust and consistent algorithm that adapts to prediction accuracy, achieving near-optimal competitive ratios and nearly matching lower bounds for the problem.

Findings

Achieves a competitive ratio of $O( ext{min}( ext{error}^{1/3} ext{log}^{2/3}(n), ext{sqrt(error)}, ext{sqrt}(n)))$

Algorithm is robust and consistent, performing well with accurate predictions and no worse than nonclairvoyant solutions

Lower bounds show the algorithm is nearly optimal within a class of deterministic algorithms

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 $O(\min(\eta^{1/3}\log^{2/3}(n), \sqrt{\eta}, \sqrt{n}))$, where $n$ is the number of item types and $\eta\leq n^2$ 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 $\eta < o(n^{3/2}/\log^2(n))$, 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 $\Omega(\eta^{1/3})$, so this algorithm is nearly the best possible with respect to this error metric.