LeadCache：网络中的遗憾最优缓存
LeadCache: Regret-Optimal Caching in Networks
摘要：
我们认为在网络缓存的背景下，在线预测问题。假设多个用户通过二分网络连接到多个缓存。在任何时间段，每个用户都可以请求从大型目录中选择的任意文件。如果所请求的文件被高速缓存在连接到用户的高速缓存中的至少一个中，则满足用户在槽处的请求。我们的目标是预测，预取，并以最佳方式分配文件的缓存在每个插槽，以最大限度地提高缓存命中的总数。由于目标函数的非凸性和非光滑性，该问题是非平凡的。在本文中，我们提出了$\texttt{LeadCache}$ -一个有效的在线缓存政策的基础上，跟随扰动领导者的范例。我们发现，$\texttt{LeadCache}$是遗憾最优的$\tilde{O}(n^{3/8}),$的一个因素，其中$n$是用户的数量。我们设计了两个有效的实现的$\texttt{LeadCache}$政策，一个基于Pipage舍入和其他基于Madow的采样，其中每一个都使得每一个迭代一次调用LP求解器。此外，与强定律型的假设，我们表明，在$\texttt{LeadCache}$下的文件提取的总数仍然几乎肯定有限的无限地平线。最后，我们利用图着色的结果得到了一个近似紧的后悔下界。我们的结论是，基于学习的$\texttt{LeadCache}$政策决定性地优于国家的最先进的缓存政策在理论上和经验。
英文摘要：
We consider an online prediction problem in the context of network caching. Assume that multiple users are connected to several caches via a bipartite network. At any time slot, each user may request an arbitrary file chosen from a large catalog. A user's request at a slot is met if the requested file is cached in at least one of the caches connected to the user. Our objective is to predict, prefetch, and optimally distribute the files on the caches at each slot to maximize the total number of cache hits. The problem is non-trivial due to the non-convex and non-smooth nature of the objective function. In this paper, we propose $\texttt{LeadCache}$ - an efficient online caching policy based on the Follow-the-Perturbed-Leader paradigm. We show that $\texttt{LeadCache}$ is regret-optimal up to a factor of $\tilde{O}(n^{3/8}),$ where $n$ is the number of users. We design two efficient implementations of the $\texttt{LeadCache}$ policy, one based on Pipage rounding and the other based on Madow's sampling, each of which makes precisely one call to an LP-solver per iteration. Furthermore, with a Strong-Law-type assumption, we show that the total number of file fetches under $\texttt{LeadCache}$ remains almost surely finite over an infinite horizon. Finally, we derive an approximately tight regret lower bound using results from graph coloring. We conclude that the learning-based $\texttt{LeadCache}$ policy decisively outperforms the state-of-the-art caching policies both theoretically and empirically.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
