Optimal Caching for Partial-Observation Regime and Beyond

We study the caching problem from an online learning point-of-view, i.e., no model assumptions and prior knowledge for the file request sequence. Our goal is to design an efficient online caching policy with minimal regret, i.e., minimizing the total number of cache miss with respect to the best static configuration in hindsight. Previous studies, such as Follow-The-Perturbed-Leader (FTPL) and Follow-The-Regularized-Leader (FTRL) caching policies, have provided some near-optimal results, but their theoretical performance guarantees only valid for the regime wherein all arrival requests could be seen by the cache, which is not the case in some practical scenarios. Hence our work closes this gap by considering the partial-observation regime wherein only requests for currently cached files are seen by the cache, which is more challenging and has not been studied before. We propose an online caching policy integrating the FTPL with a popularity estimation procedure called Geometric Resampling (GR), which is the first no-regret policy in this regime (achieve sublinear regret guarantee). Moreover, in the partial-observation regime, we also consider the caching problem with additional operational requirements of real-world systems, i.e., long-term constraints, and proposed a modified version of FTRL combining with GR to address this challenge setting. The theoretical analysis shows that this caching policy is able to achieve no-regret guarantee while satisfying the operational long-term constraints in expectation. Finally, we conduct numerical experiments to validate the theoretical guarantees of our proposed caching policies.