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 $η\leq n^2$ 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 $η< o(n^{3/2}/\log^2(n))$, 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.

翻译：本文研究了在带截止期限的在线联合补货问题（JRP-D）中利用预测信息的方法。先前的研究表明，在先知设定下算法具有$O(1)$的渐进最优竞争比，而在非先知设定下竞争比为$O(\sqrt{n})$，其中$n$表示物品种类数。本文的目标是通过利用预测信息显著降低非先知情况下的竞争比：当请求到达时，其真实截止期限不公开，但算法会获得一个预测的截止期限。主要成果是提出一种算法，其竞争比为$O(\min(η^{1/3}\log^{2/3}(n), \sqrtη, \sqrt{n}))$，其中$n$为物品种类数，$η\leq n^2$通过“瞬时物品逆序数”量化预测的缺陷程度。因此，该算法具有鲁棒性（即不会差于非先知解）和一致性（若预测无逆序，则算法表现接近先知算法）。此外，若误差不太大（具体满足$η< o(n^{3/2}/\log^2(n))$），该算法可获得优于非先知算法的渐进竞争比。我们还证明，所有属于特定合理类别的确定性算法都具有$Ω(η^{1/3})$的竞争比下界，因此该算法在此误差度量标准下近乎最优。