Random-Mode Frank-Wolfe Algorithm for Tensor Completion in Wireless Edge Caching

Wireless edge caching is a popular strategy to avoid backhaul congestion in the next generation networks, where the content is cached in advance at the base stations to fulfil the redundant requests during peak periods. In the edge caching data, the missing observations are inevitable due to dynamic selective popularity. Among the completion methods, the tensor-based models have been shown to be the most advantageous for missing data imputation. Also, since the observations are correlated across time, files, and base stations, in this paper, we formulate the caching, prediction and recommendation problem as a fourth-order tensor completion problem. Since the content library can be large leading to a large dimension tensor, we modify the latent norm-based Frank-Wolfe (FW) algorithm with tensor-ring decomposition towards a lower time complexity using random mode selection. Analyzing the time and space complexity of the algorithm shows $N$-times reduction in computational time where $N$ is the order of tensor. Simulations with MovieLens dataset shows the approximately similar reconstruction errors for the presented FW algorithm as compared to that of the recent FW algorithm, albeit with lower computation overhead. It is also demonstrated that the completed tensor improves normalized cache hit rates for linear prediction schemes.