Abhishek Sinha

Optimal caching of files in a content distribution network (CDN) is a problem of fundamental and growing commercial interest. Although many different caching algorithms are in use today, the fundamental performance limits of the network caching algorithms from an online learning point-of-view remain poorly understood to date. In this paper, we resolve this question in the following two settings: (1) a single user connected to a single cache, and (2) a set of users and a set of caches interconnected through a bipartite network. Recently, an online gradient-based coded caching policy was shown to enjoy sub-linear regret. However, due to the lack of known regret lower bounds, the question of the optimality of the proposed policy was left open. In this paper, we settle this question by deriving tight non-asymptotic regret lower bounds in the above settings. In addition to that, we propose a new Follow-the-Perturbed-Leader-based uncoded caching policy with near-optimal regret. Technically, the lower-bounds are obtained by relating the online caching problem to the classic probabilistic paradigm of balls-into-bins. Our proofs make extensive use of a new result on the expected load in the most populated half of the bins, which might also be of independent interest. We evaluate the performance of the caching policies by experimenting with the popular MovieLens dataset and conclude the paper with design recommendations and a list of open problems.

We design efficient online scheduling policies to maximize the freshness of information delivered to the users in a cellular network under both adversarial and stochastic channel and mobility assumptions. The information freshness achieved by a policy is investigated through the lens of a recently proposed metric - Age-of-Information (AoI). We show that a natural greedy scheduling policy is competitive against any optimal offline policy in minimizing the AoI in the adversarial setting. We also derive universal lower bounds to the competitive ratio achievable by any online policy in the adversarial framework. In the stochastic setting, we show that a simple index policy is near-optimal for minimizing the average AoI in two different mobility scenarios. Further, we prove that the greedy scheduling policy minimizes the peak AoI for static users in the stochastic setting. Simulation results show that the proposed policies perform well under realistic conditions.

Optimal caching of files in a content distribution network (CDN) is a problem of fundamental and growing commercial interest. Although many different caching algorithms are in use today, the fundamental performance limits of the network caching algorithms from an online learning point-of-view remain poorly understood to date. In this paper, we resolve this question in the following two settings: (1) a single user connected to a single cache, and (2) a set of users and a set of caches interconnected through a bipartite network. Recently, an online gradient-based coded caching policy was shown to enjoy sub-linear regret. However, due to the lack of known regret lower bounds, the question of the optimality of the proposed policy was left open. In this paper, we settle this question by deriving tight non-asymptotic regret lower bounds in the above settings. In addition to that, we propose a new Follow-the- Perturbed-Leader-based uncoded caching policy with near-optimal regret. Technically, the lower-bounds are obtained by relating the online caching problem to the classic probabilistic paradigm of balls-into-bins. Our proofs make extensive use of a new result on the expected load in the most populated half of the bins, which might also be of independent interest.We evaluate the performance of the caching policies by experimenting with the popular Movie- Lens dataset and conclude the paper with design recommendations and a list of open problems.