Chen Li

Chen Li, Georg Stadler

We study sparse solutions of optimal control problems governed by PDEs with uncertain coefficients. We propose two formulations, one where the solution is a deterministic control optimizing the mean objective, and a formulation aiming at stochastic controls that share the same sparsity structure. In both formulations, regions where the controls do not vanish can be interpreted as optimal locations for placing control devices. In this paper, we focus on linear PDEs with linearly entering uncertain parameters. Under these assumptions, the deterministic formulation reduces to a problem with known structure, and thus we mainly focus on the stochastic control formulation. Here, shared sparsity is achieved by incorporating the $L^1$-norm of the mean of the pointwise squared controls in the objective. We reformulate the problem using a norm reweighting function that is defined over physical space only and thus helps to avoid approximation of the random space using samples or quadrature. We show that a fixed point algorithm applied to the norm reweighting formulation leads to a variant of the well-studied iterative reweighted least squares (IRLS) algorithm, and we propose a novel preconditioned Newton-conjugate gradient method to speed up the IRLS algorithm. We combine our algorithms with low-rank operator approximations, for which we provide estimates of the truncation error. We carefully examine the computational complexity of the resulting algorithms. The sparsity structure of the optimal controls and the performance of the solution algorithms are studied numerically using control problems governed by the Laplace and Helmholtz equations. In these experiments the Newton variant clearly outperforms the IRLS method.

Chen Li, Xiaoyu Wang, Tongyu Zong et al.

Edge caching plays an increasingly important role in boosting user content retrieval performance while reducing redundant network traffic. The effectiveness of caching ultimately hinges on the accuracy of predicting content popularity in the near future. However, at the network edge, content popularity can be extremely dynamic due to diverse user content retrieval behaviors and the low-degree of user multiplexing. It's challenging for the traditional reactive caching systems to keep up with the dynamic content popularity patterns. In this paper, we propose a novel Predictive Edge Caching (PEC) system that predicts the future content popularity using fine-grained learning models that mine sequential patterns in user content retrieval behaviors, and opportunistically prefetches contents predicted to be popular in the near future using idle network bandwidth. Through extensive experiments driven by real content retrieval traces, we demonstrate that PEC can adapt to highly dynamic content popularity, and significantly improve cache hit ratio and reduce user content retrieval latency over the state-of-art caching policies. More broadly, our study demonstrates that edge caching performance can be boosted by deep mining of user content retrieval behaviors.

Tongyu Zong, Chen Li, Yuanyuan Lei et al.

Edge caching will play a critical role in facilitating the emerging content-rich applications. However, it faces many new challenges, in particular, the highly dynamic content popularity and the heterogeneous caching configurations. In this paper, we propose Cocktail Edge Caching, that tackles the dynamic popularity and heterogeneity through ensemble learning. Instead of trying to find a single dominating caching policy for all the caching scenarios, we employ an ensemble of constituent caching policies and adaptively select the best-performing policy to control the cache. Towards this goal, we first show through formal analysis and experiments that different variations of the LFU and LRU policies have complementary performance in different caching scenarios. We further develop a novel caching algorithm that enhances LFU/LRU with deep recurrent neural network (LSTM) based time-series analysis. Finally, we develop a deep reinforcement learning agent that adaptively combines base caching policies according to their virtual hit ratios on parallel virtual caches. Through extensive experiments driven by real content requests from two large video streaming platforms, we demonstrate that CEC not only consistently outperforms all single policies, but also improves the robustness of them. CEC can be well generalized to different caching scenarios with low computation overheads for deployment.

Chen Li, Ben Adcock

In compressed sensing, it is often desirable to consider signals possessing additional structure beyond sparsity. One such structured signal model - which forms the focus of this paper - is the local sparsity in levels class. This class has recently found applications in problems such as compressive imaging, multi-sensor acquisition systems and sparse regularization in inverse problems. In this paper we present uniform recovery guarantees for this class when the measurement matrix corresponds to a subsampled isometry. We do this by establishing a variant of the standard restricted isometry property for sparse in levels vectors, known as the restricted isometry property in levels. Interestingly, besides the usual log factors, our uniform recovery guarantees are simpler and less stringent than existing nonuniform recovery guarantees. For the particular case of discrete Fourier sampling with Haar wavelet sparsity, a corollary of our main theorem yields a new recovery guarantee which improves over the current state-of-the-art.