学习增强加权寻呼
Learning-Augmented Weighted Paging
摘要：
我们考虑一个自然的半在线模型加权分页，在任何时候的算法给出的预测，可能有错误，下一次到达的每个页面。该模型的灵感来自Belady的经典优化离线算法，用于未加权分页，并将最近研究的学习增强分页模型（Lykouris和Vassilvitskii，2018）扩展到加权设置。对于完美的预测的情况下，我们提供了一个$\ell$竞争确定性和$O(\log \ell)$竞争随机算法，其中$\ell$是不同的权重类的数量。这两个边界都是紧的，并且当页面权重位于$1$和$W$之间时，分别意味着$O(\log W)$ -和$O(\log \log W)$ -竞争比。以前，不知道如何在加权设置中使用这些预测，并且仅知道$k$和$O(\log k)$的界限，其中$k$是高速缓存大小。我们的研究结果还推广到交错寻呼设置和不完美的预测的情况下，随着预测误差的增加，竞争比从$O(\ell)$和$O(\log \ell)$分别平滑地下降到$O(k)$和$O(\log k)$。我们的研究结果是基于几个见解Belady的算法的结构特性和页面到达预测的序列，以及新的潜在功能，将这些预测。对于未加权分页的情况下，结果意味着一个非常简单的潜在的功能为基础的证明Belady的算法，这可能是独立的利益的最优性。
英文摘要：
We consider a natural semi-online model for weighted paging, where at any time the algorithm is given predictions, possibly with errors, about the next arrival of each page. The model is inspired by Belady's classic optimal offline algorithm for unweighted paging, and extends the recently studied model for learning-augmented paging (Lykouris and Vassilvitskii, 2018) to the weighted setting. For the case of perfect predictions, we provide an $\ell$-competitive deterministic and an $O(\log \ell)$-competitive randomized algorithm, where $\ell$ is the number of distinct weight classes. Both these bounds are tight, and imply an $O(\log W)$- and $O(\log \log W)$-competitive ratio, respectively, when the page weights lie between $1$ and $W$. Previously, it was not known how to use these predictions in the weighted setting and only bounds of $k$ and $O(\log k)$ were known, where $k$ is the cache size. Our results also generalize to the interleaved paging setting and to the case of imperfect predictions, with the competitive ratios degrading smoothly from $O(\ell)$ and $O(\log \ell)$ to $O(k)$ and $O(\log k)$, respectively, as the prediction error increases. Our results are based on several insights on structural properties of Belady's algorithm and the sequence of page arrival predictions, and novel potential functions that incorporate these predictions. For the case of unweighted paging, the results imply a very simple potential function based proof of the optimality of Belady's algorithm, which may be of independent interest.
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