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We first study the error performances of the Vector Weak Rescaled Pure Greedy Algorithm for simultaneous approximation with respect to a dictionary D in a Hilbert space. We show that the convergence rate of the Vector Weak Rescaled Pure Greedy Algorithm on A 1 (D) and the closure of the convex hull of the dictionary D is optimal. The Vector Weak Rescaled Pure Greedy Algorithm has some advantages. It has a weaker convergence condition and a better convergence rate than the Vector Weak Pure Greedy Algorithm and is simpler than the Vector Weak Orthogonal Greedy Algorithm. Then, we design a Vector Weak Rescaled Pure Greedy Algorithm in a uniformly smooth Banach space setting. We obtain the convergence properties and error bound of the Vector Weak Rescaled Pure Greedy Algorithm in this case. The results show that the convergence rate of the VWRPGA on A 1 (D) is sharp. Similarly, the Vector Weak Rescaled Pure Greedy Algorithm is simpler than the Vector Weak Chebyshev Greedy Algorithm and the Vector Weak Relaxed Greedy Algorithm. [ABSTRACT FROM AUTHOR]

This paper revisits the temporal difference (TD) learning algorithm for the policy evaluation tasks in reinforcement learning. Typically, the performance of TD(0) and TD($\lambda$ λ ) is very sensitive to the choice of stepsizes. Oftentimes, TD(0) suffers from slow convergence. Motivated by the tight link between the TD(0) learning algorithm and the stochastic gradient methods, we develop a provably convergent adaptive projected variant of the TD(0) learning algorithm with linear function approximation that we term AdaTD(0). In contrast to the TD(0), AdaTD(0) is robust or less sensitive to the choice of stepsizes. Analytically, we establish that to reach an $\epsilon$ ε accuracy, the number of iterations needed is $\tilde{O}(\epsilon ^{-2}\ln ^4\frac{1}{\epsilon }/\ln ^4\frac{1}{\rho })$ O ˜ (ε - 2 ln 4 1 ε / ln 4 1 ρ) in the general case, where $\rho$ ρ represents the speed of the underlying Markov chain converges to the stationary distribution. This implies that the iteration complexity of AdaTD(0) is no worse than that of TD(0) in the worst case. When the stochastic semi-gradients are sparse, we provide theoretical acceleration of AdaTD(0). Going beyond TD(0), we develop an adaptive variant of TD($\lambda$ λ ), which is referred to as AdaTD($\lambda$ λ ). Empirically, we evaluate the performance of AdaTD(0) and AdaTD($\lambda$ λ ) on several standard reinforcement learning tasks, which demonstrate the effectiveness of our new approaches. [ABSTRACT FROM AUTHOR]

This article deals with nonconvex stochastic optimization problems in deep learning. Appropriate learning rates, based on theory, for adaptive-learning-rate optimization algorithms (e.g., Adam and AMSGrad) to approximate the stationary points of such problems are provided. These rates are shown to allow faster convergence than previously reported for these algorithms. Specifically, the algorithms are examined in numerical experiments on text and image classification and are shown in experiments to perform better with constant learning rates than algorithms using diminishing learning rates. [ABSTRACT FROM AUTHOR]

Many inverse problems in machine learning, system identification, and image processing include nuisance parameters, which are important for the recovering of other parameters. Separable nonlinear optimization problems fall into this category. The special separable structure in these problems has inspired several efficient optimization strategies. A well-known method is the variable projection (VP) that projects out a subset of the estimated parameters, resulting in a reduced problem that includes fewer parameters. The expectation maximization (EM) is another separated method that provides a powerful framework for the estimation of nuisance parameters. The relationships between EM and VP were ignored in previous studies, though they deal with a part of parameters in a similar way. In this article, we explore the internal relationships and differences between VP and EM. Unlike the algorithms that separate the parameters directly, the hierarchical identification algorithm decomposes a complex model into several linked submodels and identifies the corresponding parameters. Therefore, this article also studies the difference and connection between the hierarchical algorithm and the parameter-separated algorithms like VP and EM. In the numerical simulation part, Monte Carlo experiments are performed to further compare the performance of different algorithms. The results show that the VP algorithm usually converges faster than the other two algorithms and is more robust to the initial point of the parameters. [ABSTRACT FROM AUTHOR]

There is growing interest in applying distributed machine learning to edge computing, forming federated edge learning. Federated edge learning faces non-i.i.d. and heterogeneous data, and the communication between edge workers, possibly through distant locations and with unstable wireless networks, is more costly than their local computational overhead. In this work, we propose ${{\sf DONE}}$ DONE , a distributed approximate Newton-type algorithm with fast convergence rate for communication-efficient federated edge learning. First, with strongly convex and smooth loss functions, ${{\sf DONE}}$ DONE approximates the Newton direction in a distributed manner using the classical Richardson iteration on each edge worker. Second, we prove that ${{\sf DONE}}$ DONE has linear-quadratic convergence and analyze its communication complexities. Finally, the experimental results with non-i.i.d. and heterogeneous data show that ${{\sf DONE}}$ DONE attains a comparable performance to Newton's method. Notably, ${{\sf DONE}}$ DONE requires fewer communication iterations compared to distributed gradient descent and outperforms DANE, FEDL, and GIANT, state-of-the-art approaches, in the case of non-quadratic loss functions. [ABSTRACT FROM AUTHOR]

Convolutional transform learning (CTL), learning filters by minimizing the data fidelity loss function in an unsupervised way, is becoming very pervasive, resulting from keeping the best of both worlds: the benefit of unsupervised learning and the success of the convolutional neural network. There have been growing interests in developing efficient CTL algorithms. However, developing a convergent and accelerated CTL algorithm with accurate representations simultaneously with proper sparsity is an open problem. This article presents a new CTL framework with a $log$ regularizer that can not only obtain accurate representations but also yield strong sparsity. To efficiently address our nonconvex composite optimization, we propose to employ the proximal difference of the convex algorithm (PDCA) which relies on decomposing the nonconvex regularizer into the difference of two convex parts and then optimizes the convex subproblems. Furthermore, we introduce the extrapolation technology to accelerate the algorithm, leading to a fast and efficient CTL algorithm. In particular, we provide a rigorous convergence analysis for the proposed algorithm under the accelerated PDCA. The experimental results demonstrate that the proposed algorithm can converge more stably to desirable solutions with lower approximation error and simultaneously with stronger sparsity and, thus, learn filters efficiently. Meanwhile, the convergence speed is faster than the existing CTL algorithms. [ABSTRACT FROM AUTHOR]

Faced with massive data, subsampling is a commonly used technique to improve computational efficiency, and using nonuniform subsampling probabilities is an effective approach to improve estimation efficiency. For computational efficiency, subsampling is often implemented with replacement or through Poisson subsampling. However, no rigorous investigation has been performed to study the difference between the two subsampling procedures such as their estimation efficiency and computational convenience. This paper performs a comparative study on these two different sampling procedures. In the context of maximizing a general target function, we first derive asymptotic distributions for estimators obtained from the two sampling procedures. The results show that the Poisson subsampling may have a higher estimation efficiency. Based on the asymptotic distributions for both subsampling with replacement and Poisson subsampling, we derive optimal subsampling probabilities that minimize the variance functions of the subsampling estimators. These subsampling probabilities further reveal the similarities and differences between subsampling with replacement and Poisson subsampling. The theoretical characterizations and comparisons on the two subsampling procedures provide guidance to select a more appropriate subsampling approach in practice. Furthermore, practically implementable algorithms are proposed based on the optimal structural results, which are evaluated through both theoretical and empirical analyses. [ABSTRACT FROM AUTHOR]

This article investigates the finite-time distributed approximate optimization problem of higher order multiagent systems, where the local cost functions are considered to be quadratic functions. This problem is solved via penalty-function-based method. First, by the penalty-function method, a global approximate cost function is constructed. Second, nonlinear distributed optimization algorithms are proposed for higher order multiagent systems by the tool of adding a power integrator technique. In the optimization algorithms design, the gradients of the approximate cost function are utilized. Under the proposed optimization algorithms, the agents approach the approximate optimal solution in finite time. Although there exist errors (they may be called approximation errors) between the approximate minimizers and the global accurate minimizer, the approximation errors can be regulated by penalty parameter and the relationship between the bound of the approximation errors and the penalty parameter is given explicitly. Furthermore, the proposed distributed approximate optimization algorithms are applied to the optimal rendezvous problem of wheeled multimobile robots, making the mobile robots achieve approximate optimization rendezvous in finite time. The effectiveness of the proposed distributed optimization algorithms and their applications to optimal rendezvous problem are validated by simulations. [ABSTRACT FROM AUTHOR]

This paper explores the non-convex composition optimization consisting of inner and outer finite-sum functions with a large number of component functions. This problem arises in important applications such as nonlinear embedding and reinforcement learning. Although existing approaches such as stochastic gradient descent (SGD) and stochastic variance reduced gradient (SVRG) descent can be applied to solve this problem, their query complexities tend to be high, especially when the number of inner component functions is large. Therefore, to significantly improve the query complexity of current approaches, we have devised the stochastic composition via variance reduction (SCVR). What's more, we analyze the query complexity under different numbers of inner function and outer function. Based on different kinds of estimation of inner component function, we also present the SCVRII algorithm, though the order of query complexities are the same with SCVR. Additionally, we propose an extension to handle the mini-batch cases, which improve the query complexity under the optimal mini-batch size. The experimental results validate our proposed algorithms and theoretical analyses. [ABSTRACT FROM AUTHOR]

Binary optimization problems (BOPs) arise naturally in many fields, such as information retrieval, computer vision, and machine learning. Most existing binary optimization methods either use continuous relaxation which can cause large quantization errors, or incorporate a highly specific algorithm that can only be used for particular loss functions. To overcome these difficulties, we propose a novel generalized optimization method, named Alternating Binary Matrix Optimization (ABMO), for solving BOPs. ABMO can handle BOPs with/without orthogonality or linear constraints for a large class of loss functions. ABMO involves rewriting the binary, orthogonality and linear constraints for BOPs as an intersection of two closed sets, then iteratively dividing the original problems into several small optimization problems that can be solved as closed forms. To provide a strict theoretical convergence analysis, we add a sufficiently small perturbation and translate the original problem to an approximated problem whose feasible set is continuous. We not only provide rigorous mathematical proof for the convergence to a stationary and feasible point, but also derive the convergence rate of the proposed algorithm. The promising results obtained from four binary optimization tasks validate the superiority and the generality of ABMO compared with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

A weak conical greedy algorithm is introduced with respect to an arbitrary positive complete dictionary in a Hilbert space; this algorithm gives an approximation of an arbitrary space element by a combination of dictionary elements with nonnegative coefficients. The convergence of this algorithm is proved and an estimate of the convergence rate for the elements of the convex hull of the dictionary is given. [ABSTRACT FROM AUTHOR]

We consider decentralized large-scale continuous submodular constrained optimization problems over networks, where the goal is to maximize a sum of nonconvex functions with diminishing returns property. However, the computations of the projection step and the whole gradient can become prohibitive in high-dimensional constrained optimization problems. For this reason, a decentralized randomized block-coordinate Frank-Wolfe algorithm is proposed for submoduar maximization over networks by local communication and computation, which adopts the randomized block-coordinate descent and the Frank-Wolfe technique. We also show that the proposed algorithm converges to an approximation fact $(1-e^{-p_{\max }/p_{\min }})$ of the global maximal points at a rate of $\mathcal {O}(1/T)$ by choosing a suitable stepsize, where $T$ is the number of iterations. In addition, we confirm the theoretical results by experiments. [ABSTRACT FROM AUTHOR]

A new method extending the scope of the superalgebraically convergent 2-D wave diffraction algorithms is proposed. The principal tool is the construction of an infinitely smooth approximation to the boundary contour. The construction is based on the ideas of Tikhonov’s regularization to the stable summation of the Fourier series and the evaluation of unbounded operators. Both the algorithms for smoothing and the nonsaturated solutions for integral equations together provide the superalgebraic (faster than any algebraic) convergence. The comparison of the algorithms using the original (noninfinitely smooth) parameterization and the infinitely smooth one demonstrates the essential advantage of the latter over the former with respect to accuracy and time consumption. [ABSTRACT FROM AUTHOR]

This paper considers a resource allocation problem where several Internet-of-Things (IoT) devices send data to a base station (BS) with or without the help of the reconfigurable intelligent surface (RIS) assisted cellular network. The objective is to maximize the sum rate of all IoT devices by finding the optimal RIS and spreading factor (SF) for each device. Since these IoT devices lack prior information of the RISs or the channel state information (CSI), a distributed resource allocation framework with low complexity and learning features is required to achieve this goal. Therefore, we model this problem as a two-stage multi-player multi-armed bandit (MPMAB) framework to learn the optimal RIS and SF sequentially. Then, we put forth an exploration and exploitation boosting (E2Boost) algorithm to solve this two-stage MPMAB problem by combining the $\epsilon $ -greedy algorithm, Thompson sampling (TS) algorithm, and non-cooperation game method. We derive an upper regret bound for the proposed algorithm, i.e., $\mathcal {O}(\log ^{1+\delta }_{2} T)$ , increasing logarithmically with the time horizon $T$. Numerical results show that the E2Boost algorithm has the best performance among the existing methods and exhibits a fast convergence rate. More importantly, the proposed algorithm is not sensitive to the number of combinations of the RISs and SFs thanks to the two-stage allocation mechanism, which can benefit the high-density networks. [ABSTRACT FROM AUTHOR]

We analyze the orthogonal greedy algorithm when applied to dictionaries $\mathbb {D}$ whose convex hull has small entropy. We show that if the metric entropy of the convex hull of $\mathbb {D}$ decays at a rate of $O\left({n^{-\frac {1}{2}-\alpha }}\right)$ for $\alpha > 0$ , then the orthogonal greedy algorithm converges at the same rate on the variation space of $\mathbb {D}$. This improves upon the well-known $O\left({n^{-\frac {1}{2}}}\right)$ convergence rate of the orthogonal greedy algorithm in many cases, most notably for dictionaries corresponding to shallow neural networks. These results hold under no additional assumptions on the dictionary beyond the decay rate of the entropy of its convex hull. In addition, they are robust to noise in the target function and can be extended to convergence rates on the interpolation spaces of the variation norm. We show empirically that the predicted rates are obtained for the dictionary corresponding to shallow neural networks with Heaviside activation function in two dimensions. Finally, we show that these improved rates are sharp and prove a negative result showing that the iterates generated by the orthogonal greedy algorithm cannot in general be bounded in the variation norm of $\mathbb {D}$. [ABSTRACT FROM AUTHOR]

The $K$ K -means algorithm is one of the most popular clustering methods. However, it is a well-known fact that its performance, in terms of quality of the obtained solution and computational load, highly depends upon its initialization phase. For this reason, different initialization techniques have been developed throughout the years to enable its fast convergence to competitive solutions. In this sense, it is common practice to re-start the $K$ K -means algorithm several times via one of these techniques and keep the solution with the lowest error. Unfortunately, such a choice is still likely to be a poor approximation of the optimal set of centroids. In this article, we introduce a cheap Split-Merge step that can be used to re-start the $K$ K -means algorithm after reaching a fixed point. Under some settings, one can show that this approach reduces the error of the given fixed point without requiring any further iteration of the $K$ K -means algorithm. Moreover, experimental results show that this strategy is able to generate approximations with an associated error that is hard to reach for different multi-start methods, such as multi-start Forgy $K$ K -means, $K$ K -means++ and Hartigan $K$ K -means, while also computing a lower amount of distances than the previous algorithms. [ABSTRACT FROM AUTHOR]

Dual Coordinate Descent (DCD) is one of the most popular optimization methods. The parallelization of DCD is difficult, as DCD is sequential in nature. As such, simultaneously running multiple DCD threads on batches of data elements causes result inaccuracy and slow convergence, due to the concurrent updates of multiple coordinates. Some parallelization methods adopt separable approximate functions that depend on the degree of parallelism. Such dependencies result in both poor scalability and slow-convergence. To address these challenges, in this paper we present a new parallel primal-dual algorithm for DCD, called PPD. In PPD, the block data distribution is utilized to obtain a new approximate function that is independent from the parallelism. Moreover, PPD is designed with a novel primal-dual acceleration scheme to approach the optimal solution closely and quickly. We demonstrate the advantages of PPD in terms of scalability and efficiency through experiments. [ABSTRACT FROM AUTHOR]

Area coverage and network lifetime are two contradictory issues to the architecture development of a wireless sensor network (WSN). A satisfactory balance could be achieved by deploying abundant sensor nodes randomly and dividing them into $k$ exclusive cover sets. Toward self-organized partition with higher efficiency, we address the problem from the perspective of networked potential games and propose a memorial mixed-response algorithm (MMRA), which is implemented in a distributed and synchronous manner. Being viewed as a game player, each sensor node first updates its memory using a temporary action, which is generated by following a mixed response rule. After this, the coordination evolves into the next iteration by each player randomly drawing an action from its memory with equal probabilities. We prove that our algorithm converges with probability 1 to a convention of Nash equilibria, with the worst approximation ratio strictly larger than 0.5. Moreover, it is also found that a tradeoff between solution efficiency and computation time could be achieved via the adjustment of the amount of randomness introduced via the memory length $m$ as well as the probability $p_{m}$ , where better partition results are more likely to be generated using a larger $m$ and smaller $p_{m}$. Comparisons with existing distributed methods demonstrate the superiority of our method in terms of solution refinement as well as convergence speed. [ABSTRACT FROM AUTHOR]

Motivated by the recent success of reinforcement learning algorithms, this paper studies a class of biased stochastic approximation (SA) procedures under a mild “ergodicity-like” assumption on the random noise sequence. Building on a multistep Lyapunov function that looks ahead to several future updates to accommodate the stochastic perturbations (thus gaining control over the bias), we prove a general result on the convergence of the SA iterates, and use it to derive non-asymptotic bounds on the mean-square error in the case of constant stepsizes. This novel viewpoint renders finite-time analysis of biased SA algorithms under a family of stochastic perturbations possible. For direct comparison with prior work, we demonstrate these bounds by applying them to TD-learning with linear function approximation, under the Markov chain observation model. The resultant finite-time error bound for TD-learning is the first of its kind, in the sense that it holds i) for the unmodified versions (i.e., without any modification to the updates) using even nonlinear approximators; as well as for Markov chains ii) under sublinear mixing conditions and iii) starting from any initial distribution, at least one of which has to be violated for existing results to be applicable. [ABSTRACT FROM AUTHOR]

We propose two modified versions of the classical gradient ascent method to compute the capacity of finite-state channels with Markovian inputs. For the case that the channel mutual information rate is strongly concave in a parameter taking values in a compact convex subset of some Euclidean space, our first algorithm proves to achieve polynomial accuracy in polynomial time and, moreover, for some special families of finite-state channels our algorithm can achieve exponential accuracy in polynomial time under some technical conditions. For the case that the channel mutual information rate may not be strongly concave, our second algorithm proves to be at least locally convergent. [ABSTRACT FROM AUTHOR]

This article presents an improved online adaptive dynamic programming (ADP) algorithm to solve the optimal control problem of continuous-time nonlinear systems with infinite horizon cost. The Hamilton–Jacobi–Bellman (HJB) equation is iteratively approximated by a novel critic-only structure which is constructed using the single echo state network (ESN). Inspired by the dual heuristic programming (DHP) technique, ESN is designed to approximate the costate function, then to derive the optimal controller. As the ESN is characterized by the echo state property (ESP), it is proved that the ESN can successfully approximate the solution to the HJB equation. Besides, to eliminate the requirement for the initial admissible control, a new weight tuning law is designed by adding an alternative condition. The stability of the closed-loop optimal control system and the convergence of the out weights of the ESN are guaranteed by using the Lyapunov theorem in the sense of uniformly ultimately bounded (UUB). Two simulation examples, including linear system and nonlinear system, are given to illustrate the availability and effectiveness of the proposed approach by comparing it with the polynomial neural-network scheme. [ABSTRACT FROM AUTHOR]

This brief studies a rational model identification problem using a novel gradient descent algorithm. The rational model is approximated by a second-order Volterra system, whose parameters and structure are estimated through an accelerated gradient descent algorithm. This algorithm improves the convergence rates by computing an optimal step-size and introducing a preconditioning method. In addition, it can avoid the eigenvalue calculation if the preconditioning matrix is equal to the inverse of the information matrix. A numerical experiment is given to illustrate the performances of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In order to increase the nonlinear fitting performance of functional link neural network (FLNN), a novel chebyshev functional link spline neural filter (CFLSNF) to apply in system identification is proposed. Compared with the weak nonlinearity and boundedness of the fixed activation function (e.g., $sigmoid$ and $tanh$), CFLSNF has stronger nonlinear approximation ability than FLNN due to the flexible interpolation ability of spline activation function. At the same time, the proposed CFLSNF eliminates the hidden layers by using Chebyshev polynomial to extend the input space into high dimensions, which shows certain computational advantages compared with the artificial neural network (ANN) structures. Moreover, to update the weights of the CFLSNF, the CFLSNF-LMS is also developed. The stability conditions and computational complexity are studied. Besides, in order to make CFLSNF structure suitable for impulsive noise interference environment, a robust algorithm based on maximum versoria criterion is also proposed. Finally, the validity of the proposed architecture and algorithm are verified by experiments. [ABSTRACT FROM AUTHOR]

The max-cut problem addresses the problem of finding a cut for a graph that splits the graph into two subsets of vertices so that the number of edges between these two subsets is as large as possible. However, this problem is NP-Hard, which may be solved by suboptimal algorithms. In this brief, we propose a fast and accurate Riemannian optimization algorithm for solving the max-cut problem. To do so, we develop a gradient descent algorithm and prove its convergence. Our simulation results show that the proposed method is extremely efficient on some already-investigated graphs. Specifically, our method is on average 35 times faster than the best well-known techniques with slightly losing the performance, which is on average 0.96 of the max-cut value of the others. [ABSTRACT FROM AUTHOR]

Constrained reinforcement learning (CRL), also termed as safe reinforcement learning, is a promising technique enabling the deployment of RL agent in real-world systems. In this paper, we propose a successive convex approximation based off-policy optimization (SCAOPO) algorithm to solve the general CRL problem, which is formulated as a constrained Markov decision process (CMDP) in context of the average cost. The SCAOPO is based on solving a sequence of convex objective/feasibility optimization problems obtained by replacing the objective and constraint functions in the original problem with convex surrogate functions. The proposed SCAOPO enables reuse of experiences from previous updates, thereby significantly reducing implementation cost when deployed in real-world engineering systems that need to online learn the environment. In spite of the time-varying state distribution and the stochastic bias incurred by off-policy learning, the SCAOPO with a feasible initial point can still provably converge to a Karush-Kuhn-Tucker (KKT) point of the original problem almost surely. [ABSTRACT FROM AUTHOR]

One-bit compressive sensing gains its popularity in signal processing and communications due to its low storage costs and low hardware complexity. However, it has been a challenging task to recover the signal only by exploiting the one-bit (the sign) information. In this paper, we appropriately formulate the one-bit compressive sensing into a double-sparsity constrained optimization problem. The first-order optimality conditions for this nonconvex and discontinuous problem are established via the newly introduced $\tau$ -stationarity, based on which, a gradient projection subspace pursuit (GPSP) algorithm is developed. It is proven that GPSP can converge globally and terminate within finite steps. Numerical experiments have demonstrated its excellent performance in terms of a high order of accuracy with a high computational speed. [ABSTRACT FROM AUTHOR]

Optimizing non-convex functions is of primary importance in modern pattern recognition because it underlies the training of deep networks and nonlinear dimensionality reduction. First-order algorithms under suitable randomized perturbations or step-size rules have been shown to be effective for such settings as their limit points can be guaranteed to be local extrema rather than saddle points. However, it is well-known that the practical convergence of first-order methods is slower than those which exploit additional structure. In particular, empirically, successive convex approximation (SCA) converges faster than first-order methods. However, to date, SCA in general non-convex settings converges to first-order stationary points, which could either be local extrema or saddle points whose performance is typically inferior. To mitigate this issue, we propose calibrated randomized perturbations of SCA, which exhibit the improved convergence rate as compared to the gradient descent counter part. In particular, our main technical contributions are to establish the non-asymptotic performance of SCA algorithm and its perturbed variant converges to an approximate second-order stationary point. Experiments on multi-dimensional scaling, a machine learning problem whose training objective is non-convex, substantiate the performance gains associated with employing random perturbations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the policy evaluation problem in reinforcement learning with agents on a decentralized and directed network. In order to evaluate the quality of a fixed policy in this decentralized setting, one option is for agents to run decentralized temporal-difference (TD) collaboratively. To account for the practical scenarios where the state and action spaces are large and malicious attacks emerge, we focus on the decentralized TD learning with linear function approximation in the presence of malicious agents (often termed as Byzantine agents). We propose a trimmed mean-based Byzantine-resilient decentralized TD algorithm to perform policy evaluation in this setting. We establish the finite-time convergence rate, as well as the asymptotic learning error that depends on the number of Byzantine agents. Numerical experiments corroborate the robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Partitioned-block frequency-domain adaptive filter (PBFDAF) algorithms have become very popular, in particular, for acoustic signal processing. However, the stochastic behavior of PBFDAFs has not been extensively examined. This paper presents a comprehensive statistical analysis for a family of the overlap-save PBFDAF algorithms with 50% overlap, including the transient and steady-state performance. The frequency-domain equations of the PBFDAFs are transformed into the time-domain counterparts, which allows us to carry out the analysis completely in the time domain. By means of the independence assumption and vectorization operation, theoretical models for the mean and mean-square behavior of the PBFDAF algorithms are established without restricting the distribution of the inputs to being Gaussian. Specifically, the mean weight behavior and corresponding steady-state solution are provided. Closed-form expressions for the mean-square deviation (MSD) and mean-square error (MSE) are derived. The upper bound on the step size for the mean and mean-square stability of the PBFDAFs is specified. The theoretical model presents new insights into the convergence properties of the PBFDAFs with a sufficient number of coefficients. It was revealed that both the constrained and unconstrained PBFDAFs converge to the Wiener solution. However, the mean weight vector of the unconstrained PBFDAF algorithms cannot converge to the true solution for any inputs, while that of the constrained version can. The presented theory explains why the steady-state MSD of the unconstrained PBFDAF algorithm is larger than that of the constrained version but their minimum MSE is the same. Monte Carlo simulations provide very good support for our theory. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) and Kernel principal component analysis (KPCA) are fundamental methods in machine learning for dimensionality reduction. The former is a technique for finding this approximation in finite dimensions and the latter is often in an infinite dimensional reproducing Kernel Hilbert-space (RKHS). In this paper, we present a geometric framework for computing the principal linear subspaces in both (finite and infinite) situations as well as for the robust PCA case, that amounts to computing the intrinsic average on the space of all subspaces: the Grassmann manifold. Points on this manifold are defined as the subspaces spanned by $K$ K -tuples of observations. The intrinsic Grassmann average of these subspaces are shown to coincide with the principal components of the observations when they are drawn from a Gaussian distribution. We show similar results in the RKHS case and provide an efficient algorithm for computing the projection onto the this average subspace. The result is a method akin to KPCA which is substantially faster. Further, we present a novel online version of the KPCA using our geometric framework. Competitive performance of all our algorithms are demonstrated on a variety of real and synthetic data sets. [ABSTRACT FROM AUTHOR]

Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This regularizer removes the penalties on a few large-magnitude elements from the conventional $\ell _{1}$ -norm regularizer, and thus it only forces penalties on the remaining elements that are expected to be zeros. Accurate and fast reconstructions can be achieved by performing gradient projection updates within the framework of difference of convex functions (DC) programming. A double-loop algorithm and a single-loop algorithm are proposed via different DC decompositions, and these two algorithms have distinct computational complexities and convergence rates. An extension algorithm is further proposed by designing new step sizes for the single-loop algorithm. The extension algorithm has a faster convergence rate and can achieve approximately the same level of accuracy as the proposed double-loop algorithm. Numerical results show significant advantages of the proposed algorithms over existing reconstruction algorithms in terms of reconstruction accuracies and runtimes. Compared with the benchmark channel estimation approaches, the proposed algorithms can achieve smaller channel reconstruction error and higher achievable spectral efficiency. [ABSTRACT FROM AUTHOR]

This paper shows a comparison between Vector fitting and rational Krylov fitting techniques for the determination of rational models concerning the fitting accuracy, the computational performances and the model order. Primarily, the mathematics behind the second technique are presented. It should be noted that rational Krylov fitting have never been used in transmission line modeling. A new procedure is proposed to use rational Krylov fitting instead of vector fitting in the universal line model (ULM). Furthermore, it is demonstrated that this procedure has several advantages over the traditional one. Two illustrative examples involving a transmission system are presented for validation of the new procedure. [ABSTRACT FROM AUTHOR]

In this paper, we investigate resource allocation for IRS-assisted green multiuser multiple-input single-output (MISO) systems. To minimize the total transmit power, both the beamforming vectors at the access point (AP) and the phase shifts at multiple IRSs are jointly optimized, while taking into account the minimum required quality-of-service (QoS) of multiple users. First, two novel algorithms, namely a penalty-based alternating minimization (AltMin) algorithm and an inner approximation (IA) algorithm, are developed to tackle the non-convexity of the formulated optimization problem when perfect channel state information (CSI) is available. Existing designs employ semidefinite relaxation in AltMin-based algorithms, which, however, cannot ensure convergence. In contrast, the proposed penalty-based AltMin and IA algorithms are guaranteed to converge to a stationary point and a Karush-Kuhn-Tucker (KKT) solution of the design problem, respectively. Second, the impact of imperfect knowledge of the CSI of the channels between the AP and the users is investigated. To this end, a non-convex robust optimization problem is formulated and the penalty-based AltMin algorithm is extended to obtain a stationary solution. Simulation results reveal a key trade-off between the speed of convergence and the achievable total transmit power for the two proposed algorithms. In addition, we show that the proposed algorithms can significantly reduce the total transmit power at the AP compared to various baseline schemes and that the optimal numbers of transmit antennas and IRS reflecting elements, which maximize the system energy efficiency of the considered system, are finite. [ABSTRACT FROM AUTHOR]

Coupled Matrix Tensor Factorization (CMTF) facilitates the integration and analysis of multiple data sources and helps discover meaningful information. Nonnegative CMTF (N-CMTF) has been employed in many applications for identifying latent patterns, prediction, and recommendation. However, due to the added complexity with coupling between tensor and matrix data, existing N-CMTF algorithms exhibit poor computation efficiency. In this paper, a computationally efficient N-CMTF factorization algorithm is presented based on the column-wise element selection, preventing frequent gradient updates. Theoretical and empirical analyses show that the proposed N-CMTF factorization algorithm is not only more accurate but also more computationally efficient than existing algorithms in approximating the tensor as well as in identifying the underlying nature of factors. [ABSTRACT FROM AUTHOR]

Since the late 1980s, temporal difference (TD) learning has dominated the research area of policy evaluation algorithms. However, the demand for the avoidance of TD defects, such as low data-efficiency and divergence in off-policy learning, has inspired the studies of a large number of novel TD-based approaches. Gradient-based and least-squares-based algorithms comprise the major part of these new approaches. This paper aims to combine advantages of these two categories to derive an efficient policy evaluation algorithm with ${O}$ (${n} ^{ {2}}$) per-time-step runtime complexity. The least-squares-based framework is adopted, and the gradient correction is used to improve convergence performance. This paper begins with the revision of a previous ${O}$ (${n} ^{ {3}}$) batch algorithm, least-squares TD with a gradient correction (LS-TDC) to regularize the parameter vector. Based on the recursive least-squares technique, an ${O}$ (${n} ^{ {2}}$) counterpart of LS-TDC called RC is proposed. To increase data efficiency, we generalize RC with eligibility traces. An off-policy extension is also proposed based on importance sampling. In addition, the convergence analysis for RC as well as LS-TDC is given. The empirical results in both on-policy and off-policy benchmarks show that RC has a higher estimation accuracy than that of RLSTD and a significantly lower runtime complexity than that of LSTDC. [ABSTRACT FROM AUTHOR]

A rational leader selection strategy can enhance a swarm to manage the convergence and diversity during the entire search process. In this article, a novel adaptive multiobjective particle swarm optimization (MOPSO) is proposed on the basis of an evolutionary state estimation mechanism, which is used to detect the evolutionary environment whether in exploitation or exploration state. During the search process, different types of leaders, such as a convergence global best solution (c-gBest) and several diversity global best solutions (d-gBests), are to be selected from the external archive for particles under different evolutionary environments. The c-gBest is selected for improving the convergence when the swarm is in an exploitation state, while the d-gBests are chosen for enhancing the diversity in an exploration state. Furthermore, a modified archive maintenance strategy based on some predefined reference points is adopted to maximize the diversity of the Pareto solutions in the external archive. The experimental results demonstrate that the proposed algorithm performs significantly better than the several state-of-the-art multiobjective PSO algorithms and multiobjective evolutionary algorithms on 31 benchmark functions in terms of convergence and diversity of those obtained approximate Pareto fronts. [ABSTRACT FROM AUTHOR]

This brief describes a segmented structure to deal with inverse square root in floating-point digital calculation arithmetic, based on Taylor-Series expansion; it uses only the small number of their expansion terms to achieve a fast evaluation of these functions in high precision. Taylor-series expansions of the inverse square root are examined for several center points with their convergence ranges, and the inverse square root calculation algorithm trade-offs among accuracy, numbers of multiplications/additions/subtractions and LUT sizes are shown; the designer can choose the optimal algorithm for his digital inverse square root calculation, and build its conceptual dedicated hardware architecture design with the contents described here. [ABSTRACT FROM AUTHOR]

A robust adaptive filter is usually unaffected by spurious disturbances at the error sensor. In an endeavour to improve robustness of the adaptive filter, a novel modified Champernowne function (MCF) is proposed as a robust norm and the corresponding robust Champernowne adaptive filter (CMAF) is derived. To improve modelling accuracy and convergence performance for sparse systems along with being robust, a reweighted zero attraction (RZA) norm is incorporated in the cost function along with MCF and the corresponding RZA-CMAF algorithm is proposed. To further improve filter performance, the CMAF-l0 algorithm is proposed where the l0-norm is approximated using the multivariate Geman-McClure function (GMF). Bound on learning rate for the proposed algorithms is also derived. Extensive simulation study shows the improved robustness achieved by the CMAF algorithm, especially when impulsive noises are present for a longer duration. On the other hand, RZA-CMAF and CMAF-l0 can provide improved convergence performance under sparse and impulsive noise conditions, with CMAF-l0 providing the best performance. [ABSTRACT FROM AUTHOR]