We study the problem of wireless edge caching when file popularity is unknown and possibly non-stationary. A bank of $J$ caches receives file requests and a utility is accrued for each request depending on the serving cache. The network decides dynamically which files to store at each cache and how to route them, in order to maximize total utility. The request sequence is assumed to be drawn from an arbitrary distribution, capturing time-variance, temporal and spatial locality of requests. For this challenging setting, we propose the Bipartite Supergradient Caching Algorithm (BSCA) which provably exhibits no regret ( $R_{T}/T \to 0$ ). That is, as the time horizon $T$ increases, BSCA achieves (at least) the same utility with the cache configuration that we would have chosen knowing all future requests. The learning rate of the algorithm is characterized by its regret expression $R_{T}\!=\!O(\sqrt {JT})$ , which is independent of the file library size. For the single-cache case, we prove that this is the lowest attainable bound. BSCA requires at each step $J$ projections on intersections of boxes and simplices, for which we propose a tailored algorithm. Our model is the first that draws a connection between the network caching problem and Online Convex Optimization , and we demonstrate its generality by discussing various practical extensions and presenting a trace-driven comparison with state-of-the-art competitors.

中文翻译：

---

缓存网络的在线凸优化

我们研究了文件知名度未知且可能不稳定的无线边缘缓存问题。的银行 $ J $ 高速缓存接收文件请求，并根据服务高速缓存为每个请求生成实用程序。网络动态决定要在每个缓存中存储哪些文件以及如何路由它们，以最大化总实用性。假定请求序列是从任意分布中提取的，捕获了请求的时变，时间和空间局部性。对于这种具有挑战性的环境，我们建议双向超梯度缓存算法 （BSCA）可证明没有遗憾（ $ R_ {T} / T \ to 0 $ ）。也就是说，作为时间范围 $ T $ 随着BSCA的增长，（至少）实现了与缓存配置相同的效用，这与我们将来了解所有请求时选择的缓存配置相同。该算法的学习速度以其后悔表达为特征 $ R_ {T} \！= \！O（\ sqrt {JT}）$ ，这与文件库的大小无关。对于单缓存情况，我们证明这是最低的可达到范围。BSCA的每个步骤都需要 $ J $ 框和单纯形交点的投影，为此我们提出了一种量身定制的算法。我们的模型是第一个将网络缓存问题与在线凸优化 ，我们通过讨论各种实用扩展并与最新的竞争对手进行跟踪驱动的比较来证明其通用性。