论文标题

带有简洁预测的分页

Paging with Succinct Predictions

论文作者

Antoniadis, Antonios, Boyar, Joan, Eliáš, Marek, Favrholdt, Lene M., Hoeksma, Ruben, Larsen, Kim S., Polak, Adam, Simon, Bertrand

论文摘要

在在线算法领域中,分页是一个典型的问题。它在学习淘汰算法的发展中也起着核心作用,这是一项最近的研究线,旨在通过使算法访问预测来缓解经典最差分析的缺点。通常可以使用机器学习方法来生成此类预测,但是它们本质上是不完美的。先前关于学习提取的分页的工作已经调查了(i)何时再次请求当前页面(重新发生预测),(ii)最佳算法中缓存的当前状态(状态预测)(状态预测),(iii)所有请求,直到当前页面再次请求,以及(IV),以及(iv),以及(iv)。 我们从需要最少可能的预测信息的新角度研究了学习调格的分页。更具体地说,与每个页面请求一起获得的预测仅限于一点点。我们考虑了两个自然的这样的设置:(i)丢弃预测,其中预测的位表示驱逐此页面是否是``安全'',以及(ii)阶段预测,其中位表示当前页面是否在下一阶段请求(用于将输入适当分配到阶段中)。我们为两个设置中的每一种开发算法,以满足学习启发算法的所有三种理想属性 - 也就是说,尽管它们仅限于根据请求的一位预测,但它们是一致,健壮和平稳的。我们还提出了下限,以确保我们的算法绝对是最好的。

Paging is a prototypical problem in the area of online algorithms. It has also played a central role in the development of learning-augmented algorithms -- a recent line of research that aims to ameliorate the shortcomings of classical worst-case analysis by giving algorithms access to predictions. Such predictions can typically be generated using a machine learning approach, but they are inherently imperfect. Previous work on learning-augmented paging has investigated predictions on (i) when the current page will be requested again (reoccurrence predictions), (ii) the current state of the cache in an optimal algorithm (state predictions), (iii) all requests until the current page gets requested again, and (iv) the relative order in which pages are requested. We study learning-augmented paging from the new perspective of requiring the least possible amount of predicted information. More specifically, the predictions obtained alongside each page request are limited to one bit only. We consider two natural such setups: (i) discard predictions, in which the predicted bit denotes whether or not it is ``safe'' to evict this page, and (ii) phase predictions, where the bit denotes whether the current page will be requested in the next phase (for an appropriate partitioning of the input into phases). We develop algorithms for each of the two setups that satisfy all three desirable properties of learning-augmented algorithms -- that is, they are consistent, robust and smooth -- despite being limited to a one-bit prediction per request. We also present lower bounds establishing that our algorithms are essentially best possible.

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