Caching With Time-Varying Popularity Profiles: A Learning-Theoretic Perspective

Abstract

Content caching at the small-cell base stations (sBSs) in a heterogeneous wireless network is considered. A cost function is proposed that captures the backhaul link load called the "offloading loss", which measures the fraction of the requested files that are not available in the sBS caches.As opposed to the previous approaches that consider time-invariant and perfectly known popularity profile, caching with non-stationary and statistically dependent popularity profiles (assumed unknown, and hence, estimated) is studied from a learning-theoretic perspective. A probably approximately correct result is derived, which presents a high probability bound on the offloading loss difference, i.e., the error between the estimated and the optimal offloading loss. The difference is a function of the Rademacher complexity, the β−mixing coefficient, the number of time slots, and a measure of discrepancy between the estimated and true popularity profiles. A cache update algorithm is proposed, and simulation results are presented to show its superiority over periodic updates. The performance analyses for Bernoulli and Poisson request models are also presented. Index TermsCaching; time-varying popularity profiles; probably approximately correct (PAC) learning.

Dynamic Caching Content Replacement in Base Station Assisted Wireless D2D Caching Networks

“…In [32], a reinforcement learning framework was proposed while considering popularity dynamics into the analysis in order to refresh the caches in BSs and to minimize delivery cost. In [33], the loss due to outdated caching policy was analyzed for a small cell BS and an updating algorithm to minimize the offloading loss was proposed. Based on real-data observations, [34] established a workload model and then developed simple caching content replacement policies for edge-caching networks.…”

Time-Varying Mobile Edge Computing for Capacity Maximization

“…Proof: Suppose the number of users arriving in a unit of time may be 0, 1, 2, 3 • • • . The number of requests across users in any interval follows an independent Homogeneous Poisson distribution [28] and then we can record the arrival rate of users as λ in following the Homogeneous Poisson distribution. Thus, the probability that the k in users reach the BS coverage within the time interval t can be expressed as…”

“…The authors of [26] observed that most graphics density changes over time with the number of edges growing superlinearly in the number of nodes and the average distance between nodes often shrinking over time. In [27], [28], they found that in many applications, the popularity profile is unknown and changes over time; hence, they analyzed the cache with nonstationary and statistically dependent popularity profiles (hypothetically unknown and therefore estimated) from a learning theory perspective. Liu et al [29], [30] proposed a novel evolving model in which the hybrid interactions among entities, based on whether they belong to the same type, are classified into intertype and intratype interactions that are characterized by two joint graphs evolving over time.…”

Dynamic Content Updates in Heterogeneous Wireless Networks

“…To bypass this bottleneck, we note that the cost function in (3) is linear and the transition probabilities of a content does not affect the others. Hence, we can separate the value function in (7) into N independent value functions each representing a distinct content. For each content n, we have…”

“…In [6], this approach has been extended to a cooperative caching framework, where the SBSs fetch a requested content from neighboring SBSs if it is cached there. In [5], a cache replacement strategy has been introduced for time-varying popularity scenario to maximize the local service rate with a minimum replacement cost, while a more theoretical approach is taken in [7], which studies the cache update policy in the case of time-varying content popularities.…”