The design of caching algorithms to maximize hit probability has been extensively studied. In this paper, we associate each content with a utility, which is a function of either the corresponding content hit rate. We formulate a cache optimization problem to maximize the sum of utilities over all contents under stationary and ergodic request processes. This problem is non-convex in general but we reformulate it as a convex optimization problem when the inter-request time (irt) distribution has a non-increasing hazard rate function. We provide explicit optimal solutions for some irt distributions. We formulate a reverse engineering based dual implementation of LRU under stationary arrivals. We also propose online algorithms that can be implemented using limited information and use a discrete time Lyapunov technique (DTLT) to correctly characterize their stability. Informed by these results, we further propose lightweight Poisson approximate online algorithms that are accurate and efficient in achieving optimal hit rates. We compare the solutions of the hit-rate based (HRB) and hit-probability based (HPB) problems. We find that online algorithms that solve HRB are more robust than online HPB algorithms.

已经广泛研究了使命中率最大化的缓存算法的设计。在本文中，我们将每个内容与一个实用程序相关联，该实用程序是相应内容点击率的函数。我们提出了一个缓存优化问题，以使固定和遍历请求过程中所有内容的实用程序总和最大化。这个问题通常是非凸的，但是当请求间时间（irt）分布的危险率函数不增加时，我们将其重新构造为凸优化问题。我们为某些irt分布提供了明确的最佳解决方案。我们制定了在到达时基于逆向工程的LRU的双重实现。我们还提出了可以使用有限信息实现的在线算法，并使用离散时间Lyapunov技术（DTLT）来正确表征其稳定性。根据这些结果，我们进一步提出了轻量级的Poisson近似在线算法，该算法可准确有效地实现最佳命中率。我们比较了基于命中率（HRB）和基于命中概率（HPB）问题的解决方案。我们发现，解决HRB的在线算法比在线HPB算法更健壮。