发表机构
Univ. Marie et Louis Pasteur; CNRS; institut FEMTO-ST; Université de Lorraine（玛丽-路易斯·巴斯德大学; 法国国家科学研究中心; FEMTO-ST研究所; 洛林大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非先知单机调度中无法实现常数竞争比的问题，提出利用分类模型混淆矩阵构建排列不确定性集的鲁棒框架，并给出最优非自适应策略及可超越它的自适应与随机算法。
AI 中文摘要
我们研究了经典的单机调度问题，即在非先知（non-clairvoyant）环境下最小化作业完成时间之和，其中每个作业的处理时间在其完成之前一直未知。这是一个困难的问题，对于该问题不可能存在常数竞争比的算法。受鲁棒优化和学习增强算法的启发，我们引入了一种新颖的鲁棒性框架，利用分类模型提供的结构信息来克服这一限制。具体来说，我们假设作业被划分为多个类别，并且我们可以访问分类器的混淆矩阵，其条目$(k,\ell)$表示被预测属于类别$k$但实际属于类别$\ell$的作业数量。通过这种方式，我们能够将不确定性表征为每个预测类别内的排列集合，而不是离散数值场景的集合，从而避免了经典鲁棒度量（如最小最大（Min-Max）和最小最大遗憾（Min-Max Regret））的计算困难。除了这些最坏情况度量外，我们还考虑了所有场景下的期望目标。我们首先提出了一种最优的非自适应策略，该策略对上述三个鲁棒准则都是无关的（oblivious）。然后，我们研究了自适应和随机化算法，表明当矩阵具有特定结构性质时，它们可以优于最优的非自适应策略。
英文摘要
We study the classical single-machine scheduling problem of minimizing the sum of completion times of jobs in a non-clairvoyant setting, where the processing time of each job remains unknown until its completion. This is a hard problem for which no constant competitive algorithm is possible. Inspired by robust optimization and learning-augmented algorithms, we introduce a novel robustness framework that leverages structural information provided by a classification model to overcome this limitation. Specifically, we assume that jobs are partitioned into classes and we have access to the confusion matrix of the classifier, whose entry $(k,\ell)$ indicates the number of jobs predicted to belong to class~$k$ but that actually belong to class~$\ell$. In this manner, we are able to characterize uncertainty as a set of permutations within each predicted class, rather than as a collection of discrete numerical scenarios, avoiding the computational difficulty of classical robust metrics, such as Min-Max and Min-Max Regret. In addition to these worst-case metrics, we also consider the expected objective over all scenarios. We first propose an optimal non-adaptive strategy that is oblivious with respect to all three robust criteria. We then investigate adaptive and randomized algorithms, showing that they can outperform the optimal non-adaptive strategy when the matrix exhibits particular structural properties.
