On the Regret of Coded Caching with Adversarial Requests

TL;DR

This paper introduces an online learning approach to coded caching, achieving sub-linear regret against adversarial requests, and analyzes cache update costs with theoretical bounds and real-world validation.

Contribution

It presents the first study of adversarial regret in coded caching and proposes a Follow-The-Perturbed-Leader based policy with theoretical guarantees.

Findings

Achieves (\u221a T) regret for any request sequence

Provides bounds on cache update costs under different switching constraints

Validates theoretical results with real-world dataset experiments

Abstract

We study the well-known coded caching problem in an online learning framework, wherein requests arrive sequentially, and an online policy can update the cache contents based on the history of requests seen thus far. We introduce a caching policy based on the Follow-The-Perturbed-Leader principle and show that for any time horizon T and any request sequence, it achieves a sub-linear regret of \mathcal{O}(\sqrt(T) ) with respect to an oracle that knows the request sequence beforehand. Our study marks the first examination of adversarial regret in the coded caching setup. Furthermore, we also address the issue of switching cost by establishing an upper bound on the expected number of cache updates made by our algorithm under unrestricted switching and also provide an upper bound on the regret under restricted switching when cache updates can only happen in a pre-specified subset of timeslots. Finally, we validate our theoretical insights with numerical results using a real-world dataset