Regret-Optimal Online Caching for Adversarial and Stochastic Arrivals

TL;DR

This paper introduces a regret-optimal online caching policy that performs well against both adversarial and stochastic request patterns, with improved switching cost management and applicability to constrained scenarios, validated on real data.

Contribution

It proposes a Follow the Perturbed Leader-based caching policy that is simultaneously regret-optimal for adversarial and stochastic arrivals, including variants with switching costs and constraints.

Findings

Regret-optimal caching policy for both adversarial and stochastic requests.

Order-optimal performance with respect to time and switching costs.

Validated effectiveness on synthetic and real-world data.

Abstract

We consider the online caching problem for a cache of limited size. In a time-slotted system, a user requests one file from a large catalog in each slot. If the requested file is cached, the policy receives a unit reward and zero rewards otherwise. We show that a Follow the Perturbed Leader (FTPL)-based anytime caching policy is simultaneously regret-optimal for both adversarial and i.i.d. stochastic arrivals. Further, in the setting where there is a cost associated with switching the cached contents, we propose a variant of FTPL that is order-optimal with respect to time for both adversarial and stochastic arrivals and has a significantly better performance compared to FTPL with respect to the switching cost for stochastic arrivals. We also show that these results can be generalized to the setting where there are constraints on the frequency with which cache contents can be changed. Finally, we validate the results obtained on various synthetic as well as real-world traces.