We study an online caching problem in which requests can be served by a local cache to avoid retrieval costs from a remote server. The cache can update its state after a batch of requests and store an arbitrarily small fraction of each file. We study no-regret algorithms based on Online Mirror Descent (OMD) strategies. We show that bounds for the regret crucially depend on the diversity of the request process, provided by the diversity ratio 𝑅/ℎ, where 𝑅 is the size of the batch, and ℎ is the maximum multiplicity of a request in a given batch. We characterize the optimality of OMD caching policies w.r.t. regret under different diversity regimes. We also prove that, when the cache must store the entire file, rather than a fraction, OMD strategies can be coupled with a randomized rounding scheme that preserves regret guarantees, even when update costs cannot be neglected. We provide a formal characterization of the rounding problem through optimal transport theory, and moreover we propose a computationally efficient randomized rounding scheme.CCS Concepts: • Theory of computation → Caching and paging algorithms.

A similarity cache can reply to a query for an object with similar objects stored locally. In some applications of similarity caches, queries and objects are naturally represented as points in a continuous space. Examples include 360 • videos where user's head orientation-expressed in spherical coordinatesdetermines what part of the video needs to be retrieved, and recommendation systems where the objects are embedded in a finite-dimensional space with a distance metric to capture content dissimilarity. Existing similarity caching policies are simple modifications of classic policies like LRU, LFU, and qLRU and ignore the continuous nature of the space where objects are embedded. In this paper, we propose GRADES, a new similarity caching policy that uses gradient descent to navigate the continuous space and find the optimal objects to store in the cache. We provide theoretical convergence guarantees and show GRADES increases the similarity of the objects served by the cache in both applications mentioned above.

We study a cache network under arbitrary adversarial request arrivals. We propose a distributed online policy based on the online tabular greedy algorithm. Our distributed policy achieves sublinear (1-1/e)-regret, also in the case when update costs cannot be neglected. Numerical evaluation over several topologies supports our theoretical results and demonstrates that our algorithm outperforms state-of-art online cache algorithms.

We study a cache network under arbitrary adversarial request arrivals. We propose a distributed online policy based on the online tabular greedy algorithm [4]. Our distributed policy achieves sublinear (1 − 1 𝑒 )-regret, also in the case when update costs cannot be neglected. Numerical evaluation over several topologies supports our theoretical results and demonstrates that our algorithm outperforms state-of-art online cache algorithms.

We study a cache network under arbitrary adversarial request arrivals. We propose a distributed online policy based on the online tabular greedy algorithm. Our distributed policy achieves sublinear (1-1/e)-regret, also in the case when update costs cannot be neglected. Numerical evaluation over several topologies supports our theoretical results and demonstrates that our algorithm outperforms state-of-art online cache algorithms.