arXiv subjects

Zhi Zhou

Publications and source records attributed to Zhi Zhou.

At least 163 records · Page 9Linked to original sources

arXiv2020

Age of Processing: Age-driven Status Sampling and Processing Offloading for Edge Computing-enabled Real-time IoT Applications

The freshness of status information is of great importance for time-critical Internet of Things (IoT) applications. A metric measuring status freshness is the age-of-information (AoI), which captures the time elapsed from the status being generated at the source node (e.g., a sensor) to the latest status update.However, in intelligent IoT applications such as video surveillance, the status information is revealed after some computation intensive and time-consuming data processing operations, which would affect the status freshness. In this paper, we propose a novel metric, age-of-processing (AoP), to quantify such status freshness, which captures the time elapsed of the newest received processed status data since it is generated. Compared with AoI, AoP further takes the data processing time into account. Since an IoT device has limited computation and energy resource, the device can choose to offload the data processing to the nearby edge server under constrained status sampling frequency.We aim to minimize the average AoP in a long-term process by jointly optimizing the status sampling frequency and processing offloading policy. We formulate this online problem as an infinite-horizon constrained Markov decision process (CMDP) with average reward criterion. We then transform the CMDP problem into an unconstrained Markov decision process (MDP) by leveraging a Lagrangian method, and propose a Lagrangian transformation framework for the original CMDP problem. Furthermore, we integrate the framework with perturbation based refinement for achieving the optimal policy of the CMDP problem. Extensive numerical evaluations show that the proposed algorithm outperforms the benchmarks, with an average AoP reduction up to 30%.

cs.NI↗

arXiv2020

HierTrain: Fast Hierarchical Edge AI Learning with Hybrid Parallelism in Mobile-Edge-Cloud Computing

Nowadays, deep neural networks (DNNs) are the core enablers for many emerging edge AI applications. Conventional approaches to training DNNs are generally implemented at central servers or cloud centers for centralized learning, which is typically time-consuming and resource-demanding due to the transmission of a large amount of data samples from the device to the remote cloud. To overcome these disadvantages, we consider accelerating the learning process of DNNs on the Mobile-Edge-Cloud Computing (MECC) paradigm. In this paper, we propose HierTrain, a hierarchical edge AI learning framework, which efficiently deploys the DNN training task over the hierarchical MECC architecture. We develop a novel \textit{hybrid parallelism} method, which is the key to HierTrain, to adaptively assign the DNN model layers and the data samples across the three levels of edge device, edge server and cloud center. We then formulate the problem of scheduling the DNN training tasks at both layer-granularity and sample-granularity. Solving this optimization problem enables us to achieve the minimum training time. We further implement a hardware prototype consisting of an edge device, an edge server and a cloud server, and conduct extensive experiments on it. Experimental results demonstrate that HierTrain can achieve up to 6.9x speedup compared to the cloud-based hierarchical training approach.

cs.NI↗

arXiv2020

DeepCP: Deep Learning Driven Cascade Prediction Based Autonomous Content Placement in Closed Social Network

Online social networks (OSNs) are emerging as the most popular mainstream platform for content cascade diffusion. In order to provide satisfactory quality of experience (QoE) for users in OSNs, much research dedicates to proactive content placement by using the propagation pattern, user's personal profiles and social relationships in open social network scenarios (e.g., Twitter and Weibo). In this paper, we take a new direction of popularity-aware content placement in a closed social network (e.g., WeChat Moment) where user's privacy is highly enhanced. We propose a novel data-driven holistic deep learning framework, namely DeepCP, for joint diffusion-aware cascade prediction and autonomous content placement without utilizing users' personal and social information. We first devise a time-window LSTM model for content popularity prediction and cascade geo-distribution estimation. Accordingly, we further propose a novel autonomous content placement mechanism CP-GAN which adopts the generative adversarial network (GAN) for agile placement decision making to reduce the content access latency and enhance users' QoE. We conduct extensive experiments using cascade diffusion traces in WeChat Moment (WM). Evaluation results corroborate that the proposed DeepCP framework can predict the content popularity with a high accuracy, generate efficient placement decision in a real-time manner, and achieve significant content access latency reduction over existing schemes.

cs.SI↗

arXiv2020

High-order Time Stepping Schemes for Semilinear Subdiffusion Equations

The aim of this paper is to develop and analyze high-order time stepping schemes for solving semilinear subdiffusion equations. We apply the $k$-step BDF convolution quadrature to discretize the time-fractional derivative with order $α\in (0,1)$, and modify the starting steps in order to achieve optimal convergence rate. This method has already been well-studied for the linear fractional evolution equations in Jin, Li and Zhou \cite{JinLiZhou:correction}, while the numerical analysis for the nonlinear problem is still missing in the literature. By splitting the nonlinear potential term into an irregular linear part and a smoother nonlinear part, and using the generating function technique, we prove that the convergence order of the corrected BDF$k$ scheme is $O(τ^{\min(k,1+2α-ε)})$, without imposing further assumption on the regularity of the solution. Numerical examples are provided to support our theoretical results.

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arXiv2020

Nonlocal-in-time dynamics and crossover of diffusive regimes

We study a simple nonlocal-in-time dynamic system proposed for the effective modeling of complex diffusive regimes in heterogeneous media. We present its solutions and their commonly studied statistics such as the mean square distance. This interesting model employs a nonlocal operator to replace the conventional first-order time-derivative. It introduces a finite memory effect of a constant length encoded through a kernel function. The nonlocal-in-time operator is related to fractional time derivatives that rely on the entire time-history on one hand, while reduces to, on the other hand, the classical time derivative if the length of the memory window diminishes. This allows us to demonstrate the effectiveness of the nonlocal-in-time model in capturing the crossover widely observed in nature between the initial sub-diffusion and the long time normal diffusion.

math.NA↗

arXiv2019

Edge AI: On-Demand Accelerating Deep Neural Network Inference via Edge Computing

As a key technology of enabling Artificial Intelligence (AI) applications in 5G era, Deep Neural Networks (DNNs) have quickly attracted widespread attention. However, it is challenging to run computation-intensive DNN-based tasks on mobile devices due to the limited computation resources. What's worse, traditional cloud-assisted DNN inference is heavily hindered by the significant wide-area network latency, leading to poor real-time performance as well as low quality of user experience. To address these challenges, in this paper, we propose Edgent, a framework that leverages edge computing for DNN collaborative inference through device-edge synergy. Edgent exploits two design knobs: (1) DNN partitioning that adaptively partitions computation between device and edge for purpose of coordinating the powerful cloud resource and the proximal edge resource for real-time DNN inference; (2) DNN right-sizing that further reduces computing latency via early exiting inference at an appropriate intermediate DNN layer. In addition, considering the potential network fluctuation in real-world deployment, Edgentis properly design to specialize for both static and dynamic network environment. Specifically, in a static environment where the bandwidth changes slowly, Edgent derives the best configurations with the assist of regression-based prediction models, while in a dynamic environment where the bandwidth varies dramatically, Edgent generates the best execution plan through the online change point detection algorithm that maps the current bandwidth state to the optimal configuration. We implement Edgent prototype based on the Raspberry Pi and the desktop PC and the extensive experimental evaluations demonstrate Edgent's effectiveness in enabling on-demand low-latency edge intelligence.

cs.NI↗

arXiv2019

Time-Fractional Allen-Cahn Equations: Analysis and Numerical Methods

In this work, we consider a time-fractional Allen-Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order $α\in(0,1)$. First, the well-posedness and (limited) smoothing property are systematically analyzed, by using the maximal $L^p$ regularity of fractional evolution equations and the fractional Grönwall's inequality. We also show the maximum principle like their conventional local-in-time counterpart. Precisely, the time-fractional equation preserves the property that the solution only takes value between the wells of the double-well potential when the initial data does the same. Second, after discretizing the fractional derivative by backward Euler convolution quadrature, we develop several unconditionally solvable and stable time stepping schemes, i.e., convex splitting scheme, weighted convex splitting scheme and linear weighted stabilized scheme. Meanwhile, we study the discrete energy dissipation property (in a weighted average sense), which is important for gradient flow type models, for the two weighted schemes. Finally, by using a discrete version of fractional Grönwall's inequality and maximal $\ell^p$ regularity, we prove that the convergence rates of those time-stepping schemes are $O(τ^α)$ without any extra regularity assumption on the solution. We also present extensive numerical results to support our theoretical findings and to offer new insight on the time-fractional Allen-Cahn dynamics.

math.NA↗

arXiv2019

Edge Intelligence: Paving the Last Mile of Artificial Intelligence with Edge Computing

With the breakthroughs in deep learning, the recent years have witnessed a booming of artificial intelligence (AI) applications and services, spanning from personal assistant to recommendation systems to video/audio surveillance. More recently, with the proliferation of mobile computing and Internet-of-Things (IoT), billions of mobile and IoT devices are connected to the Internet, generating zillions Bytes of data at the network edge. Driving by this trend, there is an urgent need to push the AI frontiers to the network edge so as to fully unleash the potential of the edge big data. To meet this demand, edge computing, an emerging paradigm that pushes computing tasks and services from the network core to the network edge, has been widely recognized as a promising solution. The resulted new inter-discipline, edge AI or edge intelligence, is beginning to receive a tremendous amount of interest. However, research on edge intelligence is still in its infancy stage, and a dedicated venue for exchanging the recent advances of edge intelligence is highly desired by both the computer system and artificial intelligence communities. To this end, we conduct a comprehensive survey of the recent research efforts on edge intelligence. Specifically, we first review the background and motivation for artificial intelligence running at the network edge. We then provide an overview of the overarching architectures, frameworks and emerging key technologies for deep learning model towards training/inference at the network edge. Finally, we discuss future research opportunities on edge intelligence. We believe that this survey will elicit escalating attentions, stimulate fruitful discussions and inspire further research ideas on edge intelligence.

cs.DC↗

arXiv2018

Edge Intelligence: On-Demand Deep Learning Model Co-Inference with Device-Edge Synergy

As the backbone technology of machine learning, deep neural networks (DNNs) have have quickly ascended to the spotlight. Running DNNs on resource-constrained mobile devices is, however, by no means trivial, since it incurs high performance and energy overhead. While offloading DNNs to the cloud for execution suffers unpredictable performance, due to the uncontrolled long wide-area network latency. To address these challenges, in this paper, we propose Edgent, a collaborative and on-demand DNN co-inference framework with device-edge synergy. Edgent pursues two design knobs: (1) DNN partitioning that adaptively partitions DNN computation between device and edge, in order to leverage hybrid computation resources in proximity for real-time DNN inference. (2) DNN right-sizing that accelerates DNN inference through early-exit at a proper intermediate DNN layer to further reduce the computation latency. The prototype implementation and extensive evaluations based on Raspberry Pi demonstrate Edgent's effectiveness in enabling on-demand low-latency edge intelligence.

cs.DC↗

arXiv2018

Stochastic representation of solution to nonlocal-in-time diffusion

The aim of this paper is to give a stochastic representation for the solution to a natural extension of the Caputo-type evolution equation. The nonlocal-in-time operator is defined by a hypersingular integral with a (possibly time-dependent) kernel function, and it results in a model which serves a bridge between normal diffusion and anomalous diffusion. We derive the stochastic representation for the weak solution of the nonlocal-in-time problem in case of nonsmooth data. We do so by starting from an auxiliary Caputo-type evolution equation with a specific forcing term. Numerical simulations are also provided to support our theoretical results.

math.AP↗

arXiv2018

Numerical Approximation of Stochastic Time-Fractional Diffusion

We develop and analyze a numerical method for stochastic time-fractional diffusion driven by additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative of order $α\in(0,1)$, and fractionally integrated Gaussian noise (with a Riemann-Liouville fractional integral of order $γ\in[0,1]$ in the front). The numerical scheme approximates the model in space by the Galerkin method with continuous piecewise linear finite elements and in time by the classical Grünwald-Letnikov method, and the noise by the $L^2$-projection. Sharp strong and weak convergence rates are established, using suitable nonsmooth data error estimates for the deterministic counterpart. Numerical results are presented to support the theoretical findings.

math.NA↗

arXiv2018

Subdiffusion with a time-dependent coefficient: analysis and numerical solution

In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear finite elements in space and backward Euler convolution quadrature in time. The regularity of the solutions of the subdiffusion model is proved for both nonsmooth initial data and incompatible source term. Optimal-order convergence of the numerical solutions is established using the proven solution regularity and a novel perturbation argument via freezing the diffusion coefficient at a fixed time. The analysis is supported by numerical experiments.

math.NA↗

arXiv2018

Follow Me at the Edge: Mobility-Aware Dynamic Service Placement for Mobile Edge Computing

Mobile edge computing is a new computing paradigm, which pushes cloud computing capabilities away from the centralized cloud to the network edge. However, with the sinking of computing capabilities, the new challenge incurred by user mobility arises: since end-users typically move erratically, the services should be dynamically migrated among multiple edges to maintain the service performance, i.e., user-perceived latency. Tackling this problem is non-trivial since frequent service migration would greatly increase the operational cost. To address this challenge in terms of the performance-cost trade-off, in this paper we study the mobile edge service performance optimization problem under long-term cost budget constraint. To address user mobility which is typically unpredictable, we apply Lyapunov optimization to decompose the long-term optimization problem into a series of real-time optimization problems which do not require a priori knowledge such as user mobility. As the decomposed problem is NP-hard, we first design an approximation algorithm based on Markov approximation to seek a near-optimal solution. To make our solution scalable and amenable to future 5G application scenario with large-scale user devices, we further propose a distributed approximation scheme with greatly reduced time complexity, based on the technique of best response update. Rigorous theoretical analysis and extensive evaluations demonstrate the efficacy of the proposed centralized and distributed schemes.

cs.NI↗

arXiv2018

Efficient Resource Allocation for On-Demand Mobile-Edge Cloud Computing

Mobile-edge cloud computing is a new paradigm to provide cloud computing capabilities at the edge of pervasive radio access networks in close proximity to mobile users. Aiming at provisioning flexible on-demand mobile-edge cloud service, in this paper we propose a comprehensive framework consisting of a resource-efficient computation offloading mechanism for users and a joint communication and computation (JCC) resource allocation mechanism for network operator. Specifically, we first study the resource-efficient computation offloading problem for a user, in order to reduce user's resource occupation by determining its optimal communication and computation resource profile with minimum resource occupation and meanwhile satisfying the QoS constraint. We then tackle the critical problem of user admission control for JCC resource allocation, in order to properly select the set of users for resource demand satisfaction. We show the admission control problem is NP-hard, and hence develop an efficient approximation solution of a low complexity by carefully designing the user ranking criteria and rigourously derive its performance guarantee. To prevent the manipulation that some users may untruthfully report their valuations in acquiring mobile-edge cloud service, we further resort to the powerful tool of critical value approach to design truthful pricing scheme for JCC resource allocation. Extensive performance evaluation demonstrates that the proposed schemes can achieve superior performance for on-demand mobile-edge cloud computing.

cs.DC↗

arXiv2018

Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview

Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $α\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology and finance. Thus, it is of paramount importance to develop and to analyze efficient and accurate numerical methods for reliably simulating such models, and the literature on the topic is vast and fast growing. The present paper gives a concise overview on numerical schemes for the subdiffusion model with nonsmooth problem data, which are important for the numerical analysis of many problems arising in optimal control, inverse problems and stochastic analysis. We focus on the following aspects of the subdiffusion model: regularity theory, Galerkin finite element discretization in space, time-stepping schemes (including convolution quadrature and L1 type schemes), and space-time variational formulations, and compare the results with that for standard parabolic problems. Further, these aspects are showcased with illustrative numerical experiments and complemented with perspectives and pointers to relevant literature.

math.NA↗

arXiv2017

Pointwise-in-time error estimates for an optimal control problem with subdiffusion constraint

In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $α\in(0,1)$ in time. The fully discrete scheme is obtained by applying the conforming linear Galerkin finite element method in space, L1 scheme/backward Euler convolution quadrature in time, and the control variable by a variational type discretization. With a space mesh size $h$ and time stepsize $τ$, we establish the following order of convergence for the numerical solutions of the optimal control problem: $O(τ^{\min({1}/{2}+α-ε,1)}+h^2)$ in the discrete $L^2(0,T;L^2(Ω))$ norm and $O(τ^{α-ε}+\ell_h^2h^2)$ in the discrete $L^\infty(0,T;L^2(Ω))$ norm, with any small $ε>0$ and $\ell_h=\ln(2+1/h)$. The analysis relies essentially on the maximal $L^p$-regularity and its discrete analogue for the subdiffusion problem. Numerical experiments are provided to support the theoretical results.

math.NA↗

arXiv2017

Numerical analysis of nonlinear subdiffusion equations

We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $α\in(0,1)$ in time. The framework relies on three technical tools: a fractional version of the discrete Grönwall-type inequality, discrete maximal regularity, and regularity theory of nonlinear equations. We establish a general criterion for showing the fractional discrete Grönwall inequality, and verify it for the L1 scheme and convolution quadrature generated by BDFs. Further, we provide a complete solution theory, e.g., existence, uniqueness and regularity, for a time-fractional diffusion equation with a Lipschitz nonlinear source term. Together with the known results of discrete maximal regularity, we derive pointwise $L^2(Ω)$ norm error estimates for semidiscrete Galerkin finite element solutions and fully discrete solutions, which are of order $O(h^2)$ (up to a logarithmic factor) and $O(τ^α)$, respectively, without any extra regularity assumption on the solution or compatibility condition on the problem data. The sharpness of the convergence rates is supported by the numerical experiments.

math.NA↗

arXiv2017

Space-Time Petrov-Galerkin FEM for Fractional Diffusion Problems

We present and analyze a space-time Petrov-Galerkin finite element method for a time-fractional diffusion equation involving a Riemann-Liouville fractional derivative of order $α\in(0,1)$ in time and zero initial data. We derive a proper weak formulation involving different solution and test spaces and show the inf-sup condition for the bilinear form and thus its well-posedness. Further, we develop a novel finite element formulation, show the well-posedness of the discrete problem, and establish error bounds in both energy and $L^2$ norms for the finite element solution. In the proof of the discrete inf-sup condition, a certain nonstandard $L^2$ stability property of the $L^2$ projection operator plays a key role. We provide extensive numerical examples to verify the convergence of the method.

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