P. Zhang

Thomas Y. Hou, D. Huang, K. C. Lam et al.

In this paper, we propose an adaptive fast solver for a general class of symmetric positive definite (SPD) matrices which include the well-known graph Laplacian. We achieve this by developing an adaptive operator compression scheme and a multiresolution matrix factorization algorithm which achieve nearly optimal performance on both complexity and well-posedness. To develop our adaptive operator compression and multiresolution matrix factorization methods, we first introduce a novel notion of energy decomposition for SPD matrix $A$ using the representation of energy elements. The interaction between these energy elements depicts the underlying topological structure of the operator. This concept of decomposition naturally reflects the hidden geometric structure of the operator which inherits the localities of the structure. By utilizing the intrinsic geometric information under this Energy framework, we propose a systematic operator compression scheme for the inverse operator $A^{-1}$. In particular, with an appropriate partition of the underlying geometric structure, we can construct localized basis by using the concept of interior and closed energy. Meanwhile, two important localized quantities are introduced, namely the error factor and the condition factor. Our error analysis results show that these two factors will be the guidelines for finding the appropriate partition of the basis functions such that prescribed compression error and acceptable condition number can be achieved. By virtue of this insight, we propose the Patch Pairing algorithm to realize our energy partition framework for operator compression with controllable compression error and condition number.

Y. Li, X. Qin, J. Geng et al.

Participant selection (PS) helps to accelerate federated learning (FL) convergence, which is essential for the practical deployment of FL over mobile devices. While most existing PS approaches focus on improving training accuracy and efficiency rather than residual energy of mobile devices, which fundamentally determines whether the selected devices can participate. Meanwhile, the impacts of mobile devices' heterogeneous wireless transmission rates on PS and FL training efficiency are largely ignored. Moreover, PS causes the staleness issue. Prior research exploits isolated functions to force long-neglected devices to participate, which is decoupled from original PS designs. In this paper, we propose a residual energy and wireless aware PS design for efficient FL training over mobile devices (REWAFL). REW AFL introduces a novel PS utility function that jointly considers global FL training utilities and local energy utility, which integrates energy consumption and residual battery energy of candidate mobile devices. Under the proposed PS utility function framework, REW AFL further presents a residual energy and wireless aware local computing policy. Besides, REWAFL buries the staleness solution into its utility function and local computing policy. The experimental results show that REW AFL is effective in improving training accuracy and efficiency, while avoiding "flat battery" of mobile devices.

Y. Li, X. Qin, H. Chen et al.

Federated Learning (FL) over wireless network enables data-conscious services by leveraging the ubiquitous intelligence at network edge for privacy-preserving model training. As the proliferation of context-aware services, the diversified personal preferences causes disagreeing conditional distributions among user data, which leads to poor inference performance. In this sense, clustered federated learning is proposed to group user devices with similar preference and provide each cluster with a personalized model. This calls for innovative design in edge association that involves user clustering and also resource management optimization. We formulate an accuracy-cost trade-off optimization problem by jointly considering model accuracy, communication resource allocation and energy consumption. To comply with parameter encryption techniques in FL, we propose an iterative solution procedure which employs deep reinforcement learning based approach at cloud server for edge association. The reward function consists of minimized energy consumption at each base station and the averaged model accuracy of all users. Under our proposed solution, multiple edge base station are fully exploited to realize cost efficient personalized federated learning without any prior knowledge on model parameters. Simulation results show that our proposed strategy outperforms existing strategies in achieving accurate learning at low energy cost.