Efficient Regret-Optimal Online Caching

We focus on the online caching problem with a catalog of N equal-sized files and a cache that can store up to K files at a time. We consider a time-slotted system with the cache receiving one request per slot. We consider two types of request arrival processes: stochastic arrivals, where requests are generated by an i.i.d. process with an unknown distribution, and adversarial arrivals where we make no structural assumptions on the arrival process. We use regret as the performance metric to evaluate caching policies. It is known that Follow the Perturbed Leader (FTPL) has order-optimal regret performance for both stochastic and adversarial arrivals. A key limitation of FTPL is its ${\mathcal {O}}{(N)}$ computational complexity, which can be prohibitively large for applications with huge catalogs. To address this, we propose a novel variant of FTPL and show that it has the same regret performance at a significantly lower computational complexity of ${\mathcal {O}}{(K)}$ . We supplement our analytical results with simulations using synthetic and trace-based arrivals.