Optimal Caching Designs for Perfect, Imperfect and Unknown File Popularity Distributions in Large-Scale Multi-Tier Wireless Networks

Most existing caching solutions for wireless networks rest on an unrealistic assumption that the file popularity distribution is perfectly known. In this paper, we consider optimal caching designs for perfect, imperfect and unknown file popularity distributions in large-scale multi-tier wireless networks. First, in the case of perfect file popularity distribution, we formulate the optimization problem to maximize the successful transmission probability (STP), which is a nonconvex problem. We develop an efficient parallel iterative algorithm to obtain a stationary point using parallel successive convex approximation (SCA). Then, in the case of imperfect file popularity distribution, we formulate the robust optimization problem to maximize the worst-case STP. To solve this challenging maximin problem, we transform it to an equivalent complementary geometric programming (CGP), and develop an efficient iterative algorithm which is shown to converge to a stationary point using SCA. To the best of our knowledge, this is the first work explicitly considering the estimation error of file popularity distribution in the optimization of caching design. Next, in the case of unknown file popularity distribution, we formulate the stochastic optimization problem to maximize the stochastic STP (i.e., the STP in the stochastic form), which is a challenging nonconvex stochastic optimization problem. Based on stochastic parallel SCA, we develop an efficient iterative algorithm to obtain a stationary point, by exploiting structural properties of the stochastic STP and making full use of instantaneous file requests. As far as we know, this is the first work considering stochastic optimization in a large-scale multi-tier wireless network. Finally, by numerical results, we show that the proposed solutions achieve significant gains over existing schemes in all three cases.Comment: 32 pages,11 figures, submitted to IEEE Transactions on Communications (major revision

Proactive Optimization with Machine Learning: Femto-caching with Future Content Popularity

Optimizing resource allocation with predicted information has shown promising gain in boosting network performance and improving user experience. Earlier research efforts focus on optimizing proactive policies under the assumption of knowing the future information. Recently, various techniques have been proposed to predict the required information, and the prediction results were then treated as the true value in the optimization, i.e., "first-predict-then-optimize". In this paper, we introduce a proactive optimization framework for anticipatory resource allocation, where the future information is implicitly predicted under the same objective with the policy optimization in a single step. An optimization problem is formulated to integrate the implicit prediction and the policy optimization, based on the conditional distribution of the future information given the historical observations. To solve such a problem, we transform it equivalently to a problem depending on the joint distribution of future and historical information. Then, we resort to unsupervised learning with neural networks to learn the proactive policy as a function of the past observations via stochastic optimization. We take proactive caching and bandwidth allocation at base stations as a concrete example, where the objective function is the conditional expectation of successful offloading probability taken over the future popularity given the historically observed popularity. We use simulation to validate the proposed framework and compare it with the "first-predict-then-optimize" strategy and a heuristic "end-to-end" optimization strategy with supervised learning.Comment: 6 pages, 3 figures, submitted to IEEE for possible publicatio

Joint Optimization of File Placement and Delivery in Cache-Assisted Wireless Networks with Limited Lifetime and Cache Space

In this paper, the scheduling of downlink file transmission in one cell with the assistance of cache nodes with finite cache space is studied. Specifically, requesting users arrive randomly and the base station (BS) reactively multicasts files to the requesting users and selected cache nodes. The latter can offload the traffic in their coverage areas from the BS. We consider the joint optimization of the abovementioned file placement and delivery within a finite lifetime subject to the cache space constraint. Within the lifetime, the allocation of multicast power and symbol number for each file transmission at the BS is formulated as a dynamic programming problem with a random stage number. Note that there are no existing solutions to this problem. We develop an asymptotically optimal solution framework by transforming the original problem to an equivalent finite-horizon Markov decision process (MDP) with a fixed stage number. A novel approximation approach is then proposed to address the curse of dimensionality, where the analytical expressions of approximate value functions are provided. We also derive analytical bounds on the exact value function and approximation error. The approximate value functions depend on some system statistics, e.g., requesting users' distribution. One reinforcement learning algorithm is proposed for the scenario where these statistics are unknown.Comment: submit to IEEE journa