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Crucial performance metrics of a caching algorithm include its ability toquickly and accurately learn a popularity distribution of requests. However, amajority of work on analytical performance analysis focuses on hit probabilityafter an asymptotically large time has elapsed. We consider an online learningviewpoint, and characterize the "regret" in terms of the finite time differencebetween the hits achieved by a candidate caching algorithm with respect to agenie-aided scheme that places the most popular items in the cache. We firstconsider the Full Observation regime wherein all requests are seen by thecache. We show that the Least Frequently Used (LFU) algorithm is able toachieve order optimal regret, which is matched by an efficient countingalgorithm design that we call LFU-Lite. We then consider the PartialObservation regime wherein only requests for items currently cached are seen bythe cache, making it similar to an online learning problem related to themulti-armed bandit problem. We show how approaching this "caching bandit" usingtraditional approaches yields either high complexity or regret, but a simplealgorithm design that exploits the structure of the distribution can ensureorder optimal regret. We conclude by illustrating our insights using numericalsimulations.

Learning to Cache and Caching to Learn: Regret Analysis of Caching Algorithms