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In this paper, we consider the problem that minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting, which arising in many contemporary applications such as machine learning, statistics, and signal/image processing. To solve this problem, we propose a new nonmonotone accelerated proximal gradient method with variable stepsize strategy. Note that incorporating inertial term into proximal gradient method is a simple and efficient acceleration technique, while the descent property of the proximal gradient algorithm will lost. In our algorithm, the iterates generated by inertial proximal gradient scheme are accepted when the objective function values decrease or increase appropriately; otherwise, the iteration point is generated by proximal gradient scheme, which makes the function values on a subset of iterates are decreasing. We also introduce a variable stepsize strategy, which does not need a line search or does not need to know the Lipschitz constant and makes the algorithm easy to implement. We show that the sequence of iterates generated by the algorithm converges to a critical point of the objective function. Further, under the assumption that the objective function satisfies the Kurdyka–Łojasiewicz inequality, we prove the convergence rates of the objective function values and the iterates. Moreover, numerical results on both convex and nonconvex problems are reported to demonstrate the effectiveness and superiority of the proposed method and stepsize strategy. [ABSTRACT FROM AUTHOR]

In this paper, we propose to extend the standard Convolutional Dictionary Learning problem to a tensor representation where the activations are constrained to be “low-rank” through a Canonical Polyadic decomposition. We show that this additional constraint increases the robustness of the CDL with respect to noise and improve the interpretability of the final results. In addition, we discuss in detail the advantages of this representation and introduce two algorithms, based on ADMM or FISTA, that efficiently solve this problem. We show that by exploiting the low rank property of activations, they achieve lower complexity than the main CDL algorithms. Finally, we evaluate our approach on a wide range of experiments, highlighting the modularity and the advantages of this tensorial low-rank formulation. [ABSTRACT FROM AUTHOR]

With growth in the number of smart devices and advancements in their hardware, in recent years, data-driven machine learning techniques have drawn significant attention. However, due to privacy and communication issues, it is not possible to collect this data at a centralized location. Federated learning is a machine learning setting where the centralized location trains a learning model over remote devices. Federated learning algorithms cannot be employed in the real world scenarios unless they consider unreliable and resource-constrained nature of the wireless medium. In this paper, we propose a federated learning algorithm that is suitable for cellular wireless networks. We prove its convergence, and provide a sub-optimal scheduling policy that improves the convergence rate. We also study the effect of local computation steps and communication steps on the convergence of the proposed algorithm. We prove, in practice, federated learning algorithms may solve a different problem than the one that they have been employed for if the unreliability of wireless channels is neglected. Finally, through numerous experiments on real and synthetic datasets, we demonstrate the convergence of our proposed algorithm. [ABSTRACT FROM AUTHOR]