Optimal caching of files in a content distribution network (CDN) is a problem of fundamental and growing commercial interest. Although many different caching algorithms are in use today, the fundamental performance limits of network caching algorithms from an online learning point-of-view remain poorly understood to date. In this paper, we resolve this question in the following two settings: (1) a single user connected to a single cache, and (2) a set of users and a set of caches interconnected through a bipartite network. Recently, an online gradient-based coded caching policy was shown to enjoy sub-linear regret. However, due to the lack of known regret lower bounds, the question of the optimality of the proposed policy was left open. In this paper, we settle this question by deriving tight non-asymptotic regret lower bounds in both of the above settings. In addition to that, we propose a new Follow-the-Perturbed-Leader-based uncoded caching policy with near-optimal regret. Technically, the lower-bounds are obtained by relating the online caching problem to the classic probabilistic paradigm of balls-into-bins. Our proofs make extensive use of a new result on the expected load in the most populated half of the bins, which might also be of independent interest. We evaluate the performance of the caching policies by experimenting with the popular MovieLens dataset and conclude the paper with design recommendations and a list of open problems.

中文翻译：

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在线网络缓存的基本限制

内容分发网络 (CDN) 中文件的最佳缓存是一个具有根本性和日益增长的商业利益的问题。尽管今天使用了许多不同的缓存算法，但从在线学习的角度来看，网络缓存算法的基本性能限制迄今为止仍然知之甚少。在本文中，我们通过以下两个设置来解决这个问题：（1）单个用户连接到单个缓存，以及（2）通过双向网络互连的一组用户和一组缓存。最近，一种基于在线梯度的编码缓存策略被证明具有亚线性遗憾。然而，由于缺乏已知的遗憾下界，所提议的策略的最优性问题仍然悬而未决。在本文中，我们通过在上述两种设置中推导出严格的非渐近后悔下界来解决这个问题。除此之外，我们提出了一种新的基于 Follow-the-Perturbed-Leader 的未编码缓存策略，具有近乎最佳的遗憾。从技术上讲，下限是通过将在线缓存问题与球入箱的经典概率范式相关联来获得的。我们的证明在人口最多的一半垃圾箱中广泛使用了预期负载的新结果，这也可能是独立的兴趣。我们通过对流行的 MovieLens 数据集进行试验来评估缓存策略的性能，并用设计建议和未解决的问题列表结束论文。下限是通过将在线缓存问题与球入箱的经典概率范式相关联来获得的。我们的证明在人口最多的一半垃圾箱中广泛使用了预期负载的新结果，这也可能是独立的兴趣。我们通过对流行的 MovieLens 数据集进行试验来评估缓存策略的性能，并用设计建议和未解决的问题列表结束论文。下限是通过将在线缓存问题与球入箱的经典概率范式相关联来获得的。我们的证明在人口最多的一半垃圾箱中广泛使用了预期负载的新结果，这也可能是独立的兴趣。我们通过对流行的 MovieLens 数据集进行试验来评估缓存策略的性能，并用设计建议和未解决的问题列表结束论文。