Regret-Optimal Online Caching for Adversarial and Stochastic Arrivals

Fathima Zarin Faizal, Nikhil Karamchandani, Sharayu Moharir

Abstract:

We consider the online caching problem for a cache of lim-
ited 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 simultane-
ously 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 fre-
quency with which cache contents can be changed. Finally, we valida