Adaptive Caching Networks With Optimality Guarantees

We study the optimal placement of content over a network of caches, a problem naturally arising in several networking applications. Given a demand of content request rates and paths followed, we wish to determine the content placement that maximizes the expected caching gain, i.e., the reduction of routing costs due to intermediate caching. The offline version of this problem is NP-hard and, in general, the demand and topology may be a priori unknown. Hence, a distributed, adaptive approximation algorithm for placing contents into caches is desired. We show that path replication, a simple algorithm frequently encountered in literature, can be arbitrarily suboptimal when combined with traditional eviction policies. We propose a distributed, adaptive algorithm that performs stochastic gradient ascent on a concave relaxation of the expected caching gain, and constructs a probabilistic content placement within a $1-1/e$ factor from the optimal, in expectation. Motivated by our analysis, we also propose a novel greedy eviction policy to be used with path replication, and show through numerical evaluations that both algorithms significantly outperform path replication with traditional eviction policies over a broad array of network topologies.