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This paper introduces a novel caching analysis that, contrary to prior work, makes no modeling assumptions for the file request sequence. We cast the caching problem in the framework of Online Linear Optimization (OLO), and introduce a class of minimum regret caching policies, which minimize the losses with respect to the best static configuration in hindsight when the request model is unknown. These policies are very important since they are robust to popularity deviations in the sense that they learn to adjust their caching decisions when the popularity model changes. We first prove a novel lower bound for the regret of any caching policy, improving existing OLO bounds for our setting. Then we show that the Online Gradient Ascent (OGA) policy guarantees a regret that matches the lower bound, hence it is universally optimal. Finally, we shift our attention to a network of caches arranged to form a bipartite graph, and show that the Bipartite Subgradient Algorithm (BSA) has no regret.

The increasing demand for mobile data is overloading the cellular infrastructure. Small cells and edge caching is being explored as an alternative, but installation and maintenance costs for sufficient coverage are significant. In this work, we perform a preliminary study of an alternative architecture based on two main ideas: (i) using vehicles as mobile caches that can be accessed by user devices; compared to small cells, vehicles are more widespread and require lower costs; (ii) combining the mobility of vehicles with delayed content access to increase the number of cache hits (and reduce the load on the infrastructure). Contrary to standard DTN-type approaches, in our system max delays are guaranteed to be kept to a few minutes (beyond this deadline, the content is fetched from the infrastructure). We first propose an analytical framework to compute the optimal number of content replicas that one should cache, in order to minimize the infrastructure load. We then investigate how to optimally refresh these caches to introduce new contents, as well as to react to the temporal variability in content popularity. Simulations suggest that our vehicular cloud considerably reduces the infrastructure load in urban settings, assuming modest penetration rates and tolerable content access delays.

Pushing popular content to cheap "helper" nodes (e.g., small cells) during off-peak hours has recently been proposed to cope with the increase in mobile data traffic. User requests can be served locally from these helper nodes, if the requested content is available in at least one of the nearby helpers. Nevertheless, the collective storage of a few nearby helper nodes does not usually suffice to achieve a high enough hit rate in practice. We propose to depart from the assumption of hard cache hits, common in existing works, and consider "soft" cache hits, where if the original content is not available, some related contents that are locally cached can be recommended instead. Given that Internet content consumption is entertainment-oriented, we argue that there exist scenarios where a user might accept an alternative content (e.g., better download rate for alternative content, low rate plans, etc.), thus avoiding to access expensive/congested links. We formulate the problem of optimal edge caching with soft cache hits in a relatively generic setup, propose efficient algorithms, and analyze the expected gains. We then show using synthetic and real datasets of related video contents that promising caching gains could be achieved in practice.

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