LeadCache: Regret-Optimal Caching in Networks

TL;DR

LeadCache is a novel online caching algorithm that achieves near-optimal regret bounds for network caching, effectively predicting and distributing files to maximize cache hits in dynamic environments.

Contribution

The paper introduces LeadCache, a regret-optimal online caching policy with efficient implementations and theoretical guarantees, advancing the state-of-the-art in network caching strategies.

Findings

LeadCache achieves regret bounds close to the theoretical lower limit.

Efficient implementations using LP-solver calls are developed.

LeadCache outperforms existing policies both theoretically and empirically.

Abstract

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.