带预测的策略性调度中一致性与鲁棒性的权衡
Consistency-Robustness Tradeoffs for Strategyproof Scheduling with Predictions
- University of Nebraska-Lincoln（内布拉斯加大学林肯分校）
- Rensselaer Polytechnic Institute（伦斯勒理工学院）
- Beijing Normal University-Zhuhai（北京师范大学珠海校区）
- Beijing Normal-Hong Kong Baptist University（北京师范大学-香港浸会大学联合国际学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对带预测的不相关机器调度，提出确定性策略性机制 EdgeSkip，实现 4-一致性和 (2n-2)-鲁棒性，并证明作业加权机制的最优权衡下界。
AI中文摘要：
我们研究了在带有预测的 \\(n\\) 台不相关机器上的策略性调度问题。每台机器由一个拥有私有处理时间的智能体控制，而机制在智能体报告之前会收到一个关于处理时间矩阵的公开预测。目标是在满足策略性的前提下最小化最大完工时间。我们通过一致性（即预测正确时的近似保证）和鲁棒性（即任意预测时的最坏情况保证）来衡量性能。我们引入了 \textsc{EdgeSkip}，它是作业加权机制类中的一个确定性策略性成员。这类机制使用依赖于预测的权重独立分配每个作业。利用根据预测计算出的多项式时间 \\(2\\)-近似参考调度和一个标准权衡参数，\textsc{EdgeSkip} 实现了 \\(4\\)-一致性 和 \\((2n-2)\\)-鲁棒性，改进了 Balkanski、Gkatzelis 和 Tan 的 \\((6,2n)\\) 保证。在没有计算限制的情况下，使用最优参考调度的 \textsc{EdgeSkip} 对于每个 \\(C>1\\) 都是 \\(C\\)-一致 和 \\(\max\{n,(n-1)C/(C-1)\}\\)-鲁棒的。我们证明了所有作业加权机制的一个匹配的信息论下界，从而确定了该类机制的精确一致性-鲁棒性权衡。对于任意的确定性策略性机制，我们为每个 \\(C>1\\) 建立了鲁棒性下界 \\(\max\{n,C/(C-1)\}\\)。我们还研究了一个容错变体，并改进了先前的保证。实验表明，我们的机制取得了良好的经验性能。
英文摘要：
We study strategyproof scheduling on \(n\) unrelated machines with predictions. Each machine is controlled by an agent with privately known processing times, while the mechanism receives a public prediction of the processing-time matrix before the agents report. The objective is to minimize the makespan subject to strategyproofness. We measure performance by consistency, the approximation guarantee for correct predictions, and robustness, the worst-case guarantee for arbitrary predictions. We introduce \textsc{EdgeSkip}, a deterministic strategyproof member of the class of job-wise weighted mechanisms. Such mechanisms allocate each job independently using prediction-dependent weights. Using a polynomial-time \(2\)-approximate reference schedule computed from the prediction and a standard tradeoff parameter, \textsc{EdgeSkip} is \(4\)-consistent and \((2n-2)\)-robust, improving on the \((6,2n)\) guarantee of Balkanski, Gkatzelis, and Tan. Without computational restrictions, \textsc{EdgeSkip} with an optimal reference schedule is \(C\)-consistent and \(\max\{n,(n-1)C/(C-1)\}\)-robust for every \(C>1\). We prove a matching information-theoretic lower bound for all job-wise weighted mechanisms, thereby determining the exact consistency--robustness tradeoff for this class. For arbitrary deterministic strategyproof mechanisms, we establish the robustness lower bound \(\max\{n,C/(C-1)\}\) for every \(C>1\). We also study an error-tolerant variant and improve upon prior guarantees. Experiments demonstrate that our mechanisms achieve good empirical performance.
