带预测的防策略调度
Strategyproof Scheduling with Predictions
摘要：
\citet{NR99}在其开创性的论文中研究了在不相关的机器上调度作业以最小化完工时间为目标的防策略机制的设计问题。他们提供了一种防策略机制，实现了一个$n$ -近似，他们大胆推测，这是任何确定性防策略调度机制可实现的最佳近似。经过二十多年的努力，$n$仍然是最知名的近似和最近的工作\citet{CKK21}已经能够证明$Ω(\sqrt{n})$近似下界的所有确定性strategyproof机制。然而，这种强烈的负面结果在很大程度上取决于使用最坏情况分析评估这些机制的性能。为了克服这种过于悲观，而且往往没有信息的最坏情况下的界限，最近的一系列工作都集中在“学习增强框架”上，其目标是利用机器学习的预测来获得改进的近似，当这些预测准确时（一致性），同时即使预测是任意错误的（鲁棒性），也能实现接近最佳的最坏情况近似。本文利用学习增强框架研究了经典的策略调度问题~ \citet{NR99}，给出了一个确定性的多项式时间策略证明机制，该机制是$6$ -一致的，并且具有$2n$ -鲁棒性.因此，我们实现了“两全其美”：一个$O(1)$的一致性和$O(n)$的鲁棒性，渐近匹配最知名的近似。然后，我们扩展这一结果，以提供更一般的最坏情况下的近似保证作为预测误差的函数。最后，我们补充我们的积极结果表明，任何$1$一致的确定性strategyproof机制具有无限的鲁棒性。
英文摘要：
In their seminal paper that initiated the field of algorithmic mechanism design, \citet{NR99} studied the problem of designing strategyproof mechanisms for scheduling jobs on unrelated machines aiming to minimize the makespan. They provided a strategyproof mechanism that achieves an $n$-approximation and they made the bold conjecture that this is the best approximation achievable by any deterministic strategyproof scheduling mechanism. After more than two decades and several efforts, $n$ remains the best known approximation and very recent work by \citet{CKK21} has been able to prove an $Ω(\sqrt{n})$ approximation lower bound for all deterministic strategyproof mechanisms. This strong negative result, however, heavily depends on the fact that the performance of these mechanisms is evaluated using worst-case analysis. To overcome such overly pessimistic, and often uninformative, worst-case bounds, a surge of recent work has focused on the ``learning-augmented framework'', whose goal is to leverage machine-learned predictions to obtain improved approximations when these predictions are accurate (consistency), while also achieving near-optimal worst-case approximations even when the predictions are arbitrarily wrong (robustness). In this work, we study the classic strategic scheduling problem of~\citet{NR99} using the learning-augmented framework and give a deterministic polynomial-time strategyproof mechanism that is $6$-consistent and $2n$-robust. We thus achieve the ``best of both worlds'': an $O(1)$ consistency and an $O(n)$ robustness that asymptotically matches the best-known approximation. We then extend this result to provide more general worst-case approximation guarantees as a function of the prediction error. Finally, we complement our positive results by showing that any $1$-consistent deterministic strategyproof mechanism has unbounded robustness.
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