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The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. In large-scale multiobjective optimization, too many decision variables hinder the convergence search of evolutionary algorithms. Reducing the search range of the decision space will significantly alleviate this puzzle. With this in mind, this paper proposes a fuzzy decision variables framework for largescale multiobjective optimization. The framework divides the entire evolutionary process into two main stages: fuzzy evolution and precise evolution. In fuzzy evolution, we blur the decision variables of the original solution to reduce the search range of the evolutionary algorithm in the decision space so that the evolutionary population can quickly converge. The degree of fuzzification gradually decreases with the evolutionary process. Once the population approximately converges, the framework will turn to precise evolution. In precise evolution, the actual decision variables of the solution are directly optimized to increase the diversity of the population so as to be closer to the true Pareto optimal front. Finally, this paper embeds some representative algorithms into the proposed framework and verifies the framework’s effectiveness through comparative experiments on various large-scale multiobjective problems with 500 to 5000 decision variables. Experimental results show that in large-scale multiobjective optimization, the framework proposed in this paper can significantly improve the performance and computational efficiency of multiobjective optimization algorithms.

The policy relevant treatment effect (PRTE) measures the average effect of switching from a status-quo policy to a counterfactual policy under consideration. Estimation of the PRTE involves estimation of multiple preliminary parameters, including propensity scores, conditional expectation functions of the outcome and covariates given the propensity score, and marginal treatment effects. These preliminary estimators can affect the asymptotic distribution of the PRTE estimator in complicated and intractable manners. In this light, we propose an orthogonal score for double debiased estimation of the PRTE, whereby the asymptotic distribution of the PRTE estimator is obtained without any influence of preliminary parameter estimators as far as they satisfy mild requirements of convergence rates. To our knowledge, this paper is the first to develop limit distribution theories for inference about the PRTE.

Thanks to the increasing number and massive coverage, delivery drones, equipped with various sensors, have demonstrated significant but unexplored potentials for large-scale and low-cost urban sensing during package delivery. In this paper, we propose novel studies on the reutilization of such delivery drone resources to fill this void in urban crowdsensing. Accounting for interdependency between flying/sensing and drone delivery weight, we jointly optimize route selection, sensing time, and delivery weight allocation, to maximize delivery and sensing utility under drones energy constraints. This problem is formulated as a non-convex mixed integer non-Linear programming problem, which is proved to be NP-hard. To address this intricate problem, we propose near-optimal algorithms that leverage the equivalent objective function construction, the local search scheme, and the alternating iteration technique. Theoretical analysis indicates that our algorithms can achieve the 1/(4+ -approximation ratio (where is an arbitrarily small positive parameter and the convergence guarantee in polynomial time, for the scenarios of fixed and adjustable delivery weights, respectively. Extensive trace-based simulations and field experiments demonstrate that ours can significantly improve the delivery & sensing utility by 124.7% and the energy utilization rate by 72.2% on average, compared with the drone delivery without reusing.

This study aims at designing a robust nonparametric identifier for a class of singular perturbed systems (SPSs) with uncertain mathematical models. The identifier structure uses a novel identifier based on a differential neural network (DNN) with rational form, which can take into account the multirate nature of SPS. The identifier uses a mixed learning law including a rational formulation of neural networks which is useful to solve the identification of the fast dynamics in the SPS dynamics. The rational form of the design is proposed in such a way that no-singularities (denominator part of the rational form never touches the origin) are allowed in the identifier dynamics. A proposed control Lyapunov function and a nonlinear parameter identification methodology yield to design the learning laws for the class of novel rational DNN which appears as the main contribution of this study. A complementary matrix inequality-based optimization method allows to get the smallest attainable convergence invariant region. A detailed implementation methodology is also given in the study with the aim of clarifying how the proposed identifier can be used in diverse SPSs. A numerical example considering the dynamics of the enzymatic-substrate-inhibitor system with uncertain dynamics is showing how to apply the DNN identifier using the multirate nature of the proposed DNN identifier for SPSs. The proposed identifier is compared to a classical identifier which is not taking into account the multirate nature of SPS. The benefits of using the rational form for the identifier are highlighted in the numerical performance comparison based on the mean square error (MSE). This example justifies the ability of the suggested identifier to reconstruct both the fast and slow dynamics of the SPS.

In inverse reinforcement learning (RL), there are two agents. An expert target agent has a performance cost function and exhibits control and state behaviors to a learner. The learner agent does not know the expert's performance cost function but seeks to reconstruct it by observing the expert's behaviors and tries to imitate these behaviors optimally by its own response. In this article, we formulate an imitation problem where the optimal performance intent of a discrete-time (DT) expert target agent is unknown to a DT Learner agent. Using only the observed expert's behavior trajectory, the learner seeks to determine a cost function that yields the same optimal feedback gain as the expert's, and thus, imitates the optimal response of the expert. We develop an inverse RL approach with a new scheme to solve the behavior imitation problem. The approach consists of a cost function update based on an extension of RL policy iteration and inverse optimal control, and a control policy update based on optimal control. Then, under this scheme, we develop an inverse reinforcement Q-learning algorithm, which is an extension of RL Q-learning. This algorithm does not require any knowledge of agent dynamics. Proofs of stability, convergence, and optimality are given. A key property about the nonunique solution is also shown. Finally, simulation experiments are presented to show the effectiveness of the new approach.

As a category of the recurrent neural network (RNN), zeroing neural network (ZNN) can effectively handle time-variant optimization issues. Compared with the fixed-parameter ZNN that needs to be adjusted frequently to achieve good performance, the conventional variable-parameter ZNN (VPZNN) does not require frequent adjustment, but its variable parameter will tend to infinity as time grows. Besides, the existing noise-tolerant ZNN model is not good enough to deal with time-varying noise. Therefore, a new-type segmented VPZNN (SVPZNN) for handling the dynamic quadratic minimization issue (DQMI) is presented in this work. Unlike the previous ZNNs, the SVPZNN includes an integral term and a nonlinear activation function, in addition to two specially constructed time-varying piecewise parameters. This structure keeps the time-varying parameters stable and makes the model have strong noise tolerance capability. Besides, theoretical analysis on SVPZNN is proposed to determine the upper bound of convergence time in the absence or presence of noise interference. Numerical simulations verify that SVPZNN has shorter convergence time and better robustness than existing ZNN models when handling DQMI.

Fog/Edge computing is a novel computing paradigm supporting resource-constrained Internet of Things (IoT) devices by the placement of their tasks on the edge and/or cloud servers. Recently, several Deep Reinforcement Learning (DRL)-based placement techniques have been proposed in fog/edge computing environments, which are only suitable for centralized setups. The training of well-performed DRL agents requires manifold training data while obtaining training data is costly. Hence, these centralized DRL-based techniques lack generalizability and quick adaptability, thus failing to efficiently tackle application placement problems. Moreover, many IoT applications are modeled as Directed Acyclic Graphs (DAGs) with diverse topologies. Satisfying dependencies of DAG-based IoT applications incur additional constraints and increase the complexity of placement problems. To overcome these challenges, we propose an actor-critic-based distributed application placement technique, working based on the IMPortance weighted Actor-Learner Architectures (IMPALA). IMPALA is known for efficient distributed experience trajectory generation that significantly reduces the exploration costs of agents. Besides, it uses an adaptive off-policy correction method for faster convergence to optimal solutions. Our technique uses recurrent layers to capture temporal behaviors of input data and a replay buffer to improve the sample efficiency. The performance results, obtained from simulation and testbed experiments, demonstrate that our technique significantly improves the execution cost of IoT applications up to 30\% compared to its counterparts., Comment: This Paper is accepted in IEEE Transactions on Mobile Computing (TMC), on 23 October 2021

This article conducts a comparative analysis to investigate the effects of different classification algorithms and structural proximity indexes on the performance of the supervised link prediction approach to anticipating technology convergence at different forecast horizons. For this, we identify relationships between technologies of interest for different time periods and compute 10 structural proximity indexes among unconnected technologies at each period. We develop a set of classification models that identify potential convergence among unconnected technologies where each model is configured differently by a classification algorithm and a combination of the proximity indexes. We compare the performance of the classification models to investigate effective combinations of classification algorithms and proximity indexes at different forecast horizons. The empirical analysis on Wikipedia articles about artificial intelligence technology indicates that random forest outperforms others in short-term forecasting while support vector machine outperforms others in mid-term forecasting. We also identify structural proximity indexes that produce higher performance when combined with the most effective algorithm at each forecast horizon. The results of this article are expected to offer guidelines for choosing classification algorithms and indexes when applying the supervised link prediction approach in anticipating technology convergence.

Relay selection solutions for underwater acoustic cooperative networks suffer significant performance degradation as they fail to adapt to incomplete information, noisy interference and overwhelming dynamics. To address this challenge, a hierarchical adversarial multi-armed bandit learning framework by proposing an online reward estimation layer is designed to improve adaptive relay decision control. In online reward estimation layer, adaptive Kalman filter estimator is developed to properly handle noisy observation to support accurate reward. Meanwhile an online predict mechanism is projected for all relays to enrich learning information. Furthermore, based on estimate error variance, an adaptive exploration structure is developed to accelerate the balance between exploration and exploitation. All gathered information are exploited to learn relay quality for the decision-making. Accordingly, we present a Hierarchical Adversarial Bandit Learning (HABL) algorithm to fully exploit the heuristic interaction between the hierarchical framework. HABL integrates reward estimation, information prediction, adaptive exploration and decision making carefully in a holistic algorithm to maximize the learning efficiency. Thereby, the HABL-based relay selection algorithm has higher system throughput and lower communication cost. Further, we rigorously analyze the convergence of HABL algorithm and give its upper bound on the cumulative regret. Finally, extensive simulations elucidate the effectiveness of the HABL.

With consideration of false data injection (FDI) on the demand side, it brings a great challenge for the optimal defensive strategy with the security issue, voltage stability, power flow, and economic cost indexes. This article proposes a Takagi-Sugeuo-Kang (TSK) fuzzy system-based reinforcement learning approach for the resilient optimal defensive strategy of interconnected microgrids. Due to FDI uncertainty of the system load, TSK-based deep deterministic policy gradient (DDPG) is proposed to learn the actor network and the critic network, where multiple indexes' assessment occurs in the critic network, and the security switching control strategy is made in the actor network. Alternating direction method of multipliers (ADMM) method is improved for policy gradient with online coordination between the actor network and the critic network learning, and its convergence and optimality are proved properly. On the basis of security switching control strategy, the penalty-based boundary intersection (PBI)-based multiobjective optimization method is utilized to solve economic cost and emission issues simultaneously with considering voltage stability and rate-of-change of frequency (RoCoF) limits. According to simulation results, it reveals that the proposed resilient optimal defensive strategy can be a viable and promising alternative for tackling uncertain attack problems on interconnected microgrids.

In order to make redundant robot manipulators (RRMs) track the complex time-varying trajectory, the motion-planning problem of RRMs can be converted into a constrained time-varying quadratic programming (TVQP) problem. By using a new punishment mechanism-combined recurrent neural network (PMRNN) proposed in this article with reference to the varying-gain neural-dynamic design (VG-NDD) formula, the TVQP problem-based motion-planning scheme can be solved and the optimal angles and velocities of joints of RRMs can also be obtained in the working space. Then, the convergence performance of the PMRNN model in solving the TVQP problem is analyzed theoretically in detail. This novel method has been substantiated to have a faster calculation speed and better accuracy than the traditional method. In addition, the PMRNN model has also been successfully applied to an actual RRM to complete an end-effector trajectory tracking task.

Engineering design is traditionally performed by hand: an expert makes design proposals based on past experience, and these proposals are then tested for compliance with certain target specifications. Testing for compliance is performed first by computer simulation using what is called a discipline model. Such a model can be implemented by finite element analysis, multibody systems approach, etc. Designs passing this simulation are then considered for physical prototyping. The overall process may take months and is a significant cost in practice. We have developed a Bayesian optimization (BO) system for partially automating this process by directly optimizing compliance with the target specification with respect to the design parameters. The proposed method is a general framework for computing the generalized inverse of a high-dimensional nonlinear function that does not require, for example,\ gradient information, which is often unavailable from discipline models. We furthermore develop a three-tier convergence criterion based on: 1) convergence to a solution optimally satisfying all specified design criteria; 2) detection that a design satisfying all criteria is infeasible; or 3) convergence to a probably approximately correct (PAC) solution. We demonstrate the proposed approach on benchmark functions and a vehicle chassis design problem motivated by an industry setting using a state-of-the-art commercial discipline model. We show that the proposed approach is general, scalable, and efficient and that the novel convergence criteria can be implemented straightforwardly based on the existing concepts and subroutines in popular BO software packages.

A fast non-negative latent factor (FNLF) model for a high-dimensional and sparse (HiDS) matrix adopts a Single Latent Factor-dependent, Non-negative, Multiplicative and Momentum-incorporated Update (SLF-NM2U) algorithm, which enables its fast convergence. It is crucial to achieve a rigorously theoretical proof regarding its fast convergence, which has not been provided in prior research. Aiming at addressing this critical issue, this work theoretically proves that with an appropriately chosen momentum coefficient, SLF-NM2U enables the fast convergence of an FNLF model in both continuous and discrete time cases. Empirical analysis of HiDS matrices generated by representative industrial applications provides empirical evidences for the theoretical proof. Hence, this study represents an important milestone in the field of HiDS matrix analysis.

This article is concerned with a fault-tolerant formation tracking problem of nonlinear systems under unknown faults, where the leader's states are only accessible to a small set of followers via a directed graph. Under these faults, not only the amplitudes but also the signs of control coefficients become time-varying and unknown. The current setting will enhance the investigated problem's practical relevance and at the same time, it poses nontrivial design challenges of distributed control algorithms and convergence analysis. To solve this problem, a novel distributed control algorithm is developed by incorporating an estimation-based control framework together with a Nussbaum gain approach to guarantee an asymptotic cooperative formation tracking of nonlinear networked systems under unknown and dynamic actuator faults. Moreover, the proposed control framework is extended to ensure an asymptotic task-space coordination of multiple manipulators under unknown actuator faults, kinematics, and dynamics. Lastly, numerical simulation results are provided to validate the effectiveness of the proposed distributed designs.

The huge amount of data produced in the 6G networks not only brings new challenges to the reliability and efficiency of mobile devices but also drives rapid development of new storage techniques. With the benefits of fast access speed and high reliability, NAND flash memory has become a promising storage solution for the 6G networks. In this paper, we investigate a protograph-coded bit-interleaved coded modulation with iterative detection and decoding (BICM-ID) utilizing irregular mapping (IM) in the NAND flash-memory systems. First, we propose an enhanced protograph-based extrinsic information transfer (EPEXIT) algorithm to facilitate the analysis of protograph codes in the IM-BICM-ID systems. With the use of EPEXIT algorithm, a simple design method is conceived for the construction of a family of high-rate protograph codes, called irregular-mapped accumulate-repeat-accumulate (IMARA) codes, which possess excellent decoding thresholds and linear-minimum-distance-growth property. Furthermore, motivated by the voltage-region iterative gain characteristics of IM-BICM-ID systems, a novel read-voltage optimization scheme is developed to acquire accurate read-voltage levels, thus minimizing the decoding thresholds (in dB) of protograph codes. Analyses and simulations indicate that the proposed IMARA-aided IM-BICM-ID scheme and read-voltage optimization scheme remarkably improve the convergence and decoding performance of flash-memory systems. Thus, the proposed protograph-coded IM-BICM-ID can be viewed as a reliable and efficient storage solution for the new-generation mobile networks, such as Internet of Vehicles.

We consider composition problems of the form , which are important for machine learning. Although gradient descent and stochastic gradient descent are straightforward solutions, the essential computation of in each single iteration is expensive, let alone for large m. In this article, we devise a stochastically controlled compositional gradient algorithm. Specifically, we introduce two variants of stochastically controlled technique to estimate the inner function G(x) and the gradient of the objective function, respectively. The computational cost is largely reduced. However, the natural needs of two stochastic subsets D1 and D2 form direct barriers to guarantee the convergence of the algorithm, especially the theoretical proof of the convergence. To this end, we present a general convergence analysis by proving and , through which the proposed method significantly improve composition algorithms under low target accuracy (i.e., 1/e≪ m or n) in both strongly convex and nonconvex settings. Comprehensive experiments demonstrate the superiority of the proposed method over existing methods.

In this article, being different from conventional time-discretization (simply called discretization) formulas, explicit linear left-and-right 5-step (ELLR5S) formulas with sixth-order precision are proposed. The general sixth-order ELLR5S formula with four variable parameters is developed first, and constraints of these four parameters are displayed to guarantee the zero stability, consistence, and convergence of the formula. Then, by choosing specific parameter values within constraints, eight specific sixth-order ELLR5S formulas are developed. The general sixth-order ELLR5S formula is further utilized to generate discrete zeroing neural network (DZNN) models for solving time-varying linear and nonlinear systems. For comparison, three conventional discretization formulas are also utilized. Theoretical analyses are presented to show the performance of ELLR5S formulas and DZNN models. Furthermore, abundant experiments, including three practical applications, that is, angle-of-arrival (AoA) localization and two redundant manipulators (PUMA560 manipulator and Kinova manipulator) control, are conducted. The synthesized results substantiate the efficacy and superiority of sixth-order ELLR5S formulas as well as the corresponding DZNN models.

Iterative learning control (ILC) relies on a finite-time interval output predictor to determine the output trajectory in each trial. Robust ILCs intend to model the uncertainties in the predictor and to guarantee the convergence of the learning process subject to such model errors. Despite the vast literature in ILCs, parameterizing the uncertainties with the stochastic errors in the predictor parameters identified from system I/O data and thus robustifying the ILC have not yet been targeted. This work is devoted to solving such problems in a data-driven fashion. The main contributions are two-fold. First, a data-driven ILC method is developed for LTI systems. The relationship is established between the errors in the predictor matrix and the stochastic disturbances to the system. Its robust monotonic convergence (RMC) is then linked with the closed-loop learning gain matrix that contains the predictor uncertainties and is analyzed based on a closed-form expectation of this gain matrix multiplied with its own transpose, that is, in a mean-square sense (MS-RMC). Second, the data-driven ILC and MS-RMC analysis are extended to nonlinear Hammerstein-Wiener (H-W) systems. The advantages of the proposed methods are finally verified via extensive simulations in terms of their convergence and uncorrelated tracking performance with the stochastic parametric uncertainties.

Limit distribution theory in the econometric literature for functional coefficient cointegrating regression is incorrect in important ways, influencing rates of convergence, distributional properties, and practical work. The correct limit theory reveals that components from both bias and variance terms contribute to variability in the asymptotics. The errors in the literature arise because random variability in the bias term has been neglected in earlier research. In stationary regression this random variability is of smaller order and can be ignored in asymptotic analysis but not without consequences for finite sample performance. Implications of the findings for rate efficient estimation are discussed. Simulations in the Online Supplement provide further evidence supporting the new limit theory in nonstationary functional coefficient regressions.

Finding optimal parameters for acceleration structures for raytracing is key to improved performance. Previous research has shown that a speedup of over 10% of rendering time is possible. Some parameters are interdependent which complicates the process of finding an optimal configuration. It is hence interesting to find them efficiently. Autotuning is an automatic optimization scheme able to search for optimal configurations and has been applied successfully to kD-trees in the past, which we apply today on BVHs. The more parameters to optimize, the more difficult it is to find optimal solutions. In this paper, we analyze in detail the behavior of the parameters and their impact on acceleration structure building and rendering time. We show the interdependence and context sensitivity (i.e., scene, viewpoint) of the parameters. Based on the use case, this allows to target only crucial parameters. Convergence speed towards an optimal configuration is essential. To find better parameters, the autotuner needs to build the acceleration structure over and over, changing parameters every time. We introduce a hybrid model-based prediction and online autotuning method to address this issue. The prediction model allows for both instantaneous near-optimal configurations when inputs are known or similar, and efficient search of the configuration space when inputs are completely new. Online autotuning outperforms configurations recommended in literature by up to 11% median. The prediction model achieves 95% of the maximum speedup of the autotuner while reducing 90% of its overhead. Thus, hybrid online autonuning enables always-on tuning in ray tracing.

By exploiting the idea employed in the spectral Dai-Yuan method by Xue et al. [IEICE Trans. Inf. Syst. 101 (12)2984-2990 (2018)] and the approach applied in the modified Hager-Zhang scheme for nonsmooth optimization [PLos ONE 11(10): e0164289 (2016)], we develop a Dai-Yuan type iterative scheme for convex constrained nonlinear monotone system. The scheme's algorithm is obtained by combining its search direction with the projection method [Kluwer Academic Publishers, pp. 355-369(1998)]. One of the new scheme's attribute is that it is derivative-free, which makes it ideal for solving non-smooth problems. Furthermore, we demonstrate the method's application in image de-blurring problems by comparing its performance with a recent effective method. By employing mild assumptions, global convergence of the scheme is determined and results of some numerical experiments show the method to be favorable compared to some recent iterative methods.

Model-free control approaches require advanced exploration-exploitation policies to achieve practical tasks such as learning to bipedal robot walk in unstructured environments. In this article, we first construct a comprehensive exploration-exploitation policy that carries quality knowledge about the long-term predictor and the control policy, and the control signal of the model-free algorithms. Therefore, the developed model-free algorithm continues exploration by adjusting its unknown parameters until the desired learning and control are accomplished. Second, we provide an utterly model-free adaptive law enriched with the exploration-exploitation policy and derived step-by-step using the exact analogy of the model-based solution. The obtained adaptive control law considers the control signal saturation and the control signal (input) delay. Performed Lyapunov stability analysis ensures the convergence of the adaptive law that can also be used for intelligent control approaches. Third, we implement the adaptive algorithm in real time on a challenging benchmark system: a fourth-order, coupled dynamics, input saturated, and time-delayed underactuated manipulator. The results show that the proposed adaptive algorithm explores larger state-action spaces and treats the vanishing gradient problem in both learning and control. Also, we notice from the results that the learning and control properties of the adaptive algorithm are optimized as required.

Edge detection is a basic problem in computer vision and image processing. The main purpose of edge detection is to identify points with obvious brightness changes in digital images. At present, there are many good detection methods, but most of them do not consider the correctness and crispness of edges at the same time. In order to address this problem, this paper proposes a method based on a deep convolution neural network. The method is mainly based on a dense network that is then combined with the single network structure of a backward refinement path module. The former can detect and retain the feature information between different layers in an image. The latter makes full use of the extracted information so that the low-level detail features and high-level abstract features can be better integrated in the final output. We tested the method on the BIPED data set. The results show that the correctness and crispness of the edges can be balanced in the detection process, and the ODS, OIS and AP of this method reach 0.888, 0.893 and 0.916, respectively. Compared with the state-of-the-art approaches, the proposed method improves the standard evaluation by 3%-5%, and the convergence speed is also significantly improved.

The emerging Federated Learning (FL) enables IoT devices to collaboratively learn a shared model based on their local datasets. However, due to end devices heterogeneity, it will magnify the inherent synchronization barrier issue of FL and result in non-negligible waiting time when local models are trained with the identical batch size. Moreover, the useless waiting time will further lead to a great strain on devices limited battery life. Herein, we aim to alleviate the negative impact of synchronization barrier through adaptive batch size during model training. When using different batch sizes, stability and convergence of the global model should be enforced by assigning appropriate learning rates on different devices. Therefore, we first study the relationship between batch size and learning rate, and formulate a scaling rule to guide the setting of learning rate in terms of batch size. Then we theoretically analyze the convergence rate of global model and obtain a convergence upper bound. On these bases, we propose an efficient algorithm that adaptively adjusts batch size with scaled learning rate for heterogeneous devices to reduce the waiting time and save battery life. We conduct extensive simulations and testbed experiments, and the experimental results demonstrate the effectiveness of our method.

Worker reliability estimation is fundamental for crowdsensing applications. This paper studies a robust feedback rating approach to estimate worker reliability. In this approach, the requester provides a feedback rating to reflect the quality of the sensor data submitted by each worker. The aggregation of each worker's historical feedback ratings serves as a reliability estimate. The challenges are: (1) Feedback ratings are subjected to noise or bias; (2) Workers cognitive bias in task selection leads to higher sensor data quality variations. We develop a mathematical model to quantify the degree of rating bias and degree of cognitive bias. We also derive sufficient conditions, under which the aggregate rating is asymptotically accurate in estimating worker reliability, via stochastic approximation techniques. These conditions identify a class of asymptotically accurate rating aggregation rules for crowdsensing applications. We further derive the minimum number of ratings needed to guarantee a given reliability estimation accuracy, via martingale theory. Via extensive experiments: (1) We reveal fundamental understandings on how various factor such as rating bias influence the minimum number of ratings needed to achieve certain accuracy; (2) Our feedback rating approach improves air quality index estimation accuracy by as high as 50% over the URP algorithm.

This technical note proposes a decentralized-partial-consensus optimization (DPCO) problem with inequality constraints. The partial-consensus matrix originating from the Laplacian matrix is constructed to tackle the partial-consensus constraints. A continuous-time algorithm based on multiple interconnected recurrent neural networks (RNNs) is derived to solve the optimization problem. In addition, based on nonsmooth analysis and Lyapunov theory, the convergence of continuous-time algorithm is further proved. Finally, several examples demonstrate the effectiveness of main results.

In this paper, a novel data offloading decision-making framework is proposed, where users have the option to partially offload their data to a complex Multi-access Edge Computing (MEC) environment, consisting of both ground and UAV-mounted MEC servers. The problem is treated under the perspective of risk-aware user behavior as captured via prospect-theoretic utility functions, while accounting for the inherent computing environment uncertainties. The UAV-mounted MEC servers act as a common pool of resources with potentially superior but uncertain payoff for the users, while the local computation and ground server alternatives constitute safe and guaranteed options, respectively. The optimal user task offloading to the available computing choices is formulated as a maximization problem of each user's satisfaction, and confronted as a non-cooperative game. The existence and uniqueness of a Pure Nash Equilibrium (PNE) are proven, and convergence to the PNE is shown. Detailed numerical results highlight the convergence of the system to the PNE in few only iterations, while the impact of user behavior heterogeneity is evaluated. The introduced framework's consideration of the user risk-aware characteristics and computing uncertainties, results to a sophisticated exploitation of the system resources, which in turn leads to superior users' experienced performance compared to alternative approaches.

In this paper, we define and introduce some new concepts of the higher order strongly general biconvex functions involving the arbitrary bifunction and a function. Some new relationships among various concepts of higher order strongly general biconvex functions have been established. It is shown that the new parallelogram laws for Banach spaces can be obtained as applications of higher order strongly affine general biconvex functions, which is itself an novel application. It is proved that the optimality conditions of the higher order strongly general biconvex functions are characterized by a class of variational inequalities, which is called the higher order strongly general bivariational inequality. Auxiliary principle technique is used to suggest an implicit method for solving strongly general bivariational inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results.

This paper highlighted on a new improvement of the salp swarm algorithm (SSA) that is taken from the behavior of salp fishes. This shows a promising result, however it suffered from some drawbacks that limited its ability. The proposed improvement of SSA is called SSA 2. In this paper the design system where the ZigBee protocol received temperature, humidity and gas from the sensors. The base station collects received data and sends it to platform in order to process these data via SSA2. This system enables the ability to monitor and track any fault that may be occurring. A new term has been developed to make the algorithm more targeted in finding the optimal answer. Moreover, the calculation results and simulation results in Matlab shows great enhancement in the accuracy and precision of the results at very fast speed for convergence compared with the original salp swarm algorithm (SSA).

This paper investigates a class of unified stochastic linear-quadratic-Gaussian (LQG) social optima problems involving a large number of weakly-coupled interactive agents under a generalized setting. For each individual agent, the control and state process enters both diffusion and drift terms in its linear dynamics, and the control weight might be indefinite in cost functional. This setup is innovative and has great theoretical and realistic significance as its applications in mathematical finance (e.g., portfolio selection in mean-variation model). Using some fully-coupled variational analysis under the person-by-person optimality principle, and the mean-field approximation method, the decentralized social control is derived by a class of new type consistency condition (CC) system for typical representative agent. Such CC system is some mean-field forward-backward stochastic differential equation (MF-FBSDE) combined with embedding representation. The well-posedness of such forward-backward stochastic differential equation (FBSDE) system is carefully examined. The related social asymptotic optimality is related to the convergence of the average of a series of weakly-coupled backward stochastic differential equation (BSDE). They are verified through some Lyapunov equations.

We consider the incremental subgradient algorithm employing dynamic step sizes for minimizing the sum of a large number of component convex functions. The dynamic step size rule was firstly introduced by Goffin and Kiwiel [Math. Program., 1999, 85(1): 207-211] for the subgradient algorithm, soon later, for the incremental subgradient algorithm by Nedic and Bertsekas in [SIAM J. Optim., 2001, 12(1): 109-138]. It was observed experimentally that the incremental approach has been very successful in solving large separable optimizations, and that the dynamic step sizes generally have better computational performance than others in the literature. In the present paper, we propose two modified dynamic step size rules for the incremental subgradient algorithm and analyse the convergence properties of them. At last, the assignment problem is considered and the incremental subgradient algorithms employing different kinds of dynamic step sizes are applied to solve the problem. The computational experiments show that the two modified ones converges dramatically faster and stabler than the corresponding one in [SIAM J. Optim., 2001, 12(1): 109-138]. Particularly, for solving large separable convex optimizations, we strongly recommend the second one (see Algorithm 3.3 in the paper) since it has interesting computational performance and is the simplest one.

Dimensionality reduction is commonly used for identifying and analyzing patterns in the visual analysis of multi-dimensional datasets. The selection of subspaces is a core building block in projecting high-dimensional data to low-dimensional space, which is usually illustrated as a scatterplot for analysts to easily understand and explore. This process involves human prior knowledge and domain-specific requirements. Thus, quantifying and tracking the changes of projections across subspaces remain challenging. Existing methods can neither quantify the subsets-based changes of dimensionality reduction results when switching subspaces nor automatically and comprehensively display overall and subtle differences among dimensionality reduction results.To address this, we developed EvoSets, a novel visual analytics system designed to help users understand how subspaces affect dimensionality reduction results. The effects are quantified based on subsets' distribution to tracking the sensitivity of dimensionality reduction results across subspaces. System supports the exploration of the overall evolution of the dimensionality reduction results for helping users track the convergence and divergence behavior changes of subsets based on an extended Bubble Sets visualization. Similarities are intuitively illustrated, and dissimilarities are highlighted among projections based on layout constraints. The usefulness and effectiveness are evaluated with a user study and two case studies on multi-dimensional datasets.

This article presents a novel adaptive controller for a small-size unmanned helicopter using the reinforcement learning (RL) control methodology. The helicopter is subject to system uncertainties and unknown external disturbances. The dynamic unmodeling uncertainties of the system are estimated online by the actor network, and the tracking performance function is optimized via the critic network. The estimation error of the actor-critic network and the external unknown disturbances are compensated via the nonlinear robust component based on the sliding mode control method. The stability of the closed-loop system and the asymptotic convergence of the attitude tracking error are proved via the Lyapunov-based stability analysis. Finally, real-time experiments are performed on a helicopter control testbed. The experimental results show that the proposed controller achieves good control performance.

For solving dynamic generalized Lyapunov equation, two robust finite-time zeroing neural network (RFTZNN) models with stationary and nonstationary parameters are generated through the usage of an improved sign-bi-power (SBP) activation function (AF). Taking differential errors and model implementation errors into account, two corresponding perturbed RFTZNN models are derived to facilitate the analyses of robustness on the two RFTZNN models. Theoretical analysis gives the quantitatively estimated upper bounds for the convergence time (UBs-CT) of the two derived models, implying a superiority of the convergence that varying parameter RFTZNN (VP-RFTZNN) possesses over the fixed parameter RFTZNN (FP-RFTZNN). When the coefficient matrices and perturbation matrices are uniformly bounded, residual error of FP-RFTZNN is bounded, whereas that of VP-RFTZNN monotonically decreases at a super-exponential rate after a finite time, and eventually converges to 0. When these matrices are bounded but not uniform, residual error of FP-RFTZNN is no longer bounded, but that of VP-RFTZNN still converges. These superiorities of VP-RFTZNN are illustrated by abundant comparative experiments, and its application value is further proved by an application to robot.

It is known that many-objective optimization problems (MaOPs) often face the difficulty of maintaining good diversity and convergence in the search process due to the high-dimensional objective space. To address this issue, this article proposes a novel multiobjective framework for many-objective optimization (Mo4Ma), which transforms the many-objective space into multiobjective space. First, the many objectives are transformed into two indicative objectives of convergence and diversity. Second, a clustering-based sequential selection strategy is put forward in the transformed multiobjective space to guide the evolutionary search process. Specifically, the selection is circularly performed on the clustered subpopulations to maintain population diversity. In each round of selection, solutions with good performance in the transformed multiobjective space will be chosen to improve the overall convergence. The Mo4Ma is a generic framework that any type of evolutionary computation algorithm can incorporate compatibly. In this article, the differential evolution (DE) is adopted as the optimizer in the Mo4Ma framework, thus resulting in an Mo4Ma-DE algorithm. Experimental results show that the Mo4Ma-DE algorithm can obtain well-converged and widely distributed Pareto solutions along with the many-objective Pareto sets of the original MaOPs. Compared with seven state-of-the-art MaOP algorithms, the proposed Mo4Ma-DE algorithm shows strong competitiveness and general better performance.

Federated Learning (FL) is a promising machine learning paradigm to cooperatively train a global model with highly distributed data located on mobile devices. Aiming to optimize the communication efficiency for gradient aggregation and model synchronization among large-scale devices, we propose a relay-assisted FL framework. By breaking the traditional transmission-order constraint and exploiting the broadcast characteristic of relay nodes, we design a novel synchronization scheme named Partial Synchronization Parallel (PSP), in which models and gradients are transmitted simultaneously and aggregated at relay nodes, resulting in traffic reduction. We prove that PSP has the same convergence rate as the sequential synchronization approaches via rigorous analysis. To further accelerate the training process, we integrate PSP with any unbiased and error-bounded compression technologies and prove that the convergence properties of the resulting scheme still hold. Extensive experiments are conducted in a distributed cluster environment with real-world datasets and the results demonstrate that our proposed approach reduces the training time up to 37\% compared to state-of-the-art methods.

In this article, we propose an active kriging-based learning method for hybrid reliability analysis (HRA) with random and interval variables. An improved sampling strategy is proposed to target the sampling areas. Samples with maximum responses greater than 0 and minimum responses less than 0 are selected and regarded as the candidate samples; then, a U-based learning function is developed in which multiple samples of the interval are considered instead of one particular sample. To terminate the proposed method, a hybrid convergence criterion is proposed. Finally, an improved optimization strategy based on the DIRECT algorithm is developed for the Monte Carlo simulation conducted for the HRA. The performance of the proposed method is demonstrated by four numerical cases. The results illustrate that the proposed method is accurate and efficient for HRA.

We study an optimal targeting problem for super-modular games with binary actions and finitely many players. The considered problem consists in the selection of a subset of players of minimum size such that, when the actions of these players are forced to a controlled value while the others are left to repeatedly play a best response action, the system will converge to the greatest Nash equilibrium of the game. Our main contributions consist in showing that the problem is NP-complete and in proposing an efficient iterative algorithm with provable convergence properties for its solution. We discuss in detail the special case of network coordination games and its relation with the notion of cohesiveness. Finally, we show with simulations the strength of our approach with respect to naive heuristics based on classical network centrality measures.

This article addresses decentralized robust portfolio optimization based on multiagent systems. Decentralized robust portfolio optimization is first formulated as two distributed minimax optimization problems in a Markowitz return-risk framework. Cooperative-competitive multiagent systems are developed and applied for solving the formulated problems. The multiagent systems are shown to be able to reach consensuses in the expected stock prices and convergence in investment allocations through both intergroup and intragroup interactions. Experimental results of the multiagent systems with stock data from four major markets are elaborated to substantiate the efficacy of multiagent systems for decentralized robust portfolio optimization.

This article proposes a novel fixed-time converging forward-backward-forward neurodynamic network (FXFNN) to deal with mixed variational inequalities (MVIs). A distinctive feature of the FXFNN is its fast and fixed-time convergence, in contrast to conventional forward-backward-forward neurodynamic network and projected neurodynamic network. It is shown that the solution of the proposed FXFNN exists uniquely and converges to the unique solution of the corresponding MVIs in fixed time under some mild conditions. It is also shown that the fixed-time convergence result obtained for the FXFNN is independent of initial conditions, unlike most of the existing asymptotical and exponential convergence results. Furthermore, the proposed FXFNN is applied in solving sparse recovery problems, variational inequalities, nonlinear complementarity problems, and min-max problems. Finally, numerical and experimental examples are presented to validate the effectiveness of the proposed neurodynamic network.

Low-rank plus sparse matrix decomposition (LSD) is an important problem in computer vision and machine learning. It has been solved using convex relaxations of the matrix rank and l0-pseudo-norm, which are the nuclear norm and l1-norm, respectively. Convex approximations are known to result in biased estimates, to overcome which, nonconvex regularizers such as weighted nuclear-norm minimization and weighted Schatten p-norm minimization have been proposed. However, works employing these regularizers have used heuristic weight-selection strategies. We propose weighted minimax-concave penalty (WMCP) as the nonconvex regularizer and show that it admits an equivalent representation that enables weight adaptation. Similarly, an equivalent representation to the weighted matrix gamma norm (WMGN) enables weight adaptation for the low-rank part. The optimization algorithms are based on the alternating direction method of multipliers technique. We show that the optimization frameworks relying on the two penalties, WMCP and WMGN, coupled with a novel iterative weight update strategy, result in accurate low-rank plus sparse matrix decomposition. The algorithms are also shown to satisfy descent properties and convergence guarantees. On the applications front, we consider the problem of foreground-background separation in video sequences. Simulation experiments and validations on standard datasets, namely, I2R, CDnet 2012, and BMC 2012 show that the proposed techniques outperform the benchmark techniques.

The general tensor-based methods can recover missing values of multidimensional images by exploiting the low-rankness on the pixel level. However, especially when considerable pixels of an image are missing, the low-rankness is not reliable on the pixel level, resulting in some details losing in their results, which hinders the performance of subsequent image applications (e.g., image recognition and segmentation). In this article, we suggest a novel multiscale feature (MSF) tensorization by exploiting the MSFs of multidimensional images, which not only helps to recover the missing values on a higher level, that is, the feature level but also benefits subsequent image applications. By exploiting the low-rankness of the resulting MSF tensor constructed by the new tensorization, we propose the convex and nonconvex MSF tensor train rank minimization (MSF-TT) to conjointly recover the MSF tensor and the corresponding original tensor in a unified framework. We develop the alternating directional method of multipliers (ADMMs) to solve the convex MSF-TT and the proximal alternating minimization (PAM) to solve the nonconvex MSF-TT. Moreover, we establish the theoretical guarantee of convergence for the PAM algorithm. Numerical examples of real-world multidimensional images show that the proposed MSF-TT outperforms other compared approaches in image recovery and the recovered MSF tensor can benefit the subsequent image recognition.

This article concerns with terminal recurrent neural network (RNN) models for time-variant computing, featuring finite-valued activation functions (AFs), and finite-time convergence of error variables. Terminal RNNs stand for specific models that admit terminal attractors, and the dynamics of each neuron retains finite-time convergence. The might-existing imperfection in solving time-variant problems, through theoretically examining the asymptotically convergent RNNs, is pointed out for which the finite-time-convergent models are most desirable. The existing AFs are summarized, and it is found that there is a lack of the AFs that take only finite values. A finitely valued terminal RNN, among others, is taken into account, which involves only basic algebraic operations and taking roots. The proposed terminal RNN model is used to solve the time-variant problems undertaken, including the time-variant quadratic programming and motion planning of redundant manipulators. The numerical results are presented to demonstrate effectiveness of the proposed neural network, by which the convergence rate is comparable with that of the existing power-rate RNN.

Regression in a sparse Bayesian learning (SBL) framework is usually formulated as a global optimization problem with a nonconvex objective function and solved in a majorization-minimization framework where the solution quality and consistency depend heavily on the initial values of the used algorithm. In view of the shortcomings, this article presents an SBL algorithm based on collaborative neurodynamic optimization (CNO) for searching global optimal solutions to the global optimization problem. The CNO system consists of a population of recurrent neural networks (RNNs) where each RNN is convergent to a local optimum to the global optimization problem. Reinitialized repetitively via particle swarm optimization with exchanged local optima information, the RNNs iteratively improve their searching performance until reaching global convergence. The proposed CNO-based SBL algorithm is almost surely convergent to a global optimal solution to the formulated global optimization problem. Two applications with experimental results on sparse signal reconstruction and partial differential equation identification are elaborated to substantiate the superiority and efficacy of the proposed method in terms of solution optimality and consistency.

How to generate more revenues is crucial to cloud providers. Evidences from the Amazon cloud system indicate that ``dynamic pricing'' would be more profitable than ``static pricing.'' The challenges are: How to set the price in real-time so to maximize revenues? How to estimate the price dependent demand so to optimize the pricing decision? We first design a discrete-time based dynamic pricing scheme and formulate a Markov decision process to characterize the evolving dynamics of the price-dependent demand. We formulate a revenue maximization framework to determine the optimal price and theoretically characterize the ``structure'' of the optimal revenue and optimal price. We apply the Q-learning to infer the optimal price from historical transaction data and derive sufficient conditions on the model to guarantee its convergence to the optimal price, but it converges slowly. To speed up the convergence, we incorporate the structure of the optimal revenue that we obtained earlier, leading to the VpQ-learning (Q-learning with value projection) algorithm. We derive sufficient conditions, under which the VpQ-learning algorithm converges to the optimal policy. Experiments on a real-world dataset show that the VpQ-learning algorithm outperforms a variety of baselines, i.e., improves the revenue by as high as 50% over the Q-learning, speedy Q-learning, and adaptive real-time dynamic programming (ARTDP), and by as high as 20% over the fixed pricing scheme.

With increasing of data size and development of multi-core computers, asynchronous parallel stochastic optimization algorithms such as KroMagnon have gained significant attention. In this paper, we propose a new Sparse approximation and asynchronous parallel Stochastic Variance Reduced Gradient (SSVRG) method for sparse and high-dimensional machine learning problems. Unlike standard SVRG and its asynchronous parallel variant, KroMagnon, the snapshot point of SSVRG is set to the average of all the iterates in the previous epoch, which allows it to take much larger learning rates and makes it more robust to the choice of learning rates. In particular, we use the sparse approximation of the popular SVRG estimator to perform completely sparse updates. Therefore, SSVRG has a much lower per-iteration computational cost than its dense counterpart, SVRG++, and is very friendly to asynchronous parallel implementation. Moreover, we provide the convergence guarantees of SSVRG for both SC and non-SC problems, while existing asynchronous algorithms (e.g., KroMagnon) only have convergence guarantees for SC problems. Finally, we extend SSVRG to non-smooth and asynchronous parallel settings. Numerical results demonstrate that SSVRG converges significantly faster than the state-of-the-art asynchronous parallel methods, e.g., KroMagnon, and is usually more than three orders of magnitude faster than SVRG++.

As the controller parameter adjustment process is simplified significantly by using learning algorithms, the studies about learning-based control attract a lot of interest in recent years. This article focuses on the intelligent servo control problem using learning from desired demonstrations. Compared with the previous studies about the learning-based servo control, a control policy using the broad learning system (BLS) is developed and first applied to a microrobotic system, since the advantages of the BLS, such as simple structure and no-requirement for retraining when new demos' data is provided. Then, the Lyapunov theory is skillfully combined with the complex learning algorithm to derive the controller parameters' constraints. Thus, the final control policy not only can obtain the movement skills of the desired demonstrations but also have the strong ability of generalization and error convergence. Finally, simulation and experimental examples verify the effectiveness of the proposed strategy using MATLAB and a microswimmer trajectory tracking system.

This paper deals with nonconvex stochastic optimization problems in deep learning and provides appropriate learning rates with which adaptive learning rate optimization algorithms, such as Adam and AMSGrad, can approximate a stationary point of the problem. In particular, constant and diminishing learning rates are provided to approximate a stationary point of the problem. Our results also guarantee that the adaptive learning rate optimization algorithms can approximate global minimizers of convex stochastic optimization problems. The adaptive learning rate optimization algorithms are examined in numerical experiments on text and image classification. The experiments show that the algorithms with constant learning rates perform better than ones with diminishing learning rates.

Entropy regularization has been extensively adopted to improve the efficiency, the stability, and the convergence of algorithms in reinforcement learning. This paper analyzes both quantitatively and qualitatively the impact of entropy regularization for mean field games (MFGs) with learning in a finite time horizon. Our study provides a theoretical justification that entropy regularization yields time-dependent policies and, furthermore, helps stabilizing and accelerating convergence to the game equilibrium. In addition, this study leads to a policy-gradient algorithm with exploration in MFG. With this algorithm, agents are able to learn the optimal exploration scheduling, with stable and fast convergence to the game equilibrium.

Checking uniform attractivity of a time-varying dynamic system without a strict Lyapunov function is challenging as it requires the characterization of the limiting behavior of a set of trajectories. In the context of hybrid nonlinear time-varying (NLTV) systems, characterizing such limiting or convergent behaviors is even harder due to the complexity stemming from both continuous-time variations as well as discrete-time jumps. In this work, an extension of the standard hybrid time domain is introduced to define limiting behaviors, using set convergence, when time approaches either positive infinity or negative infinity. In particular, it is shown how to characterize limiting behaviors under the condition that an output signal approaches zero. Such limiting behaviors and their associated limiting systems can be used to verify uniform global attractivity. Particularly, a generalization of the classic Krasovskii-LaSalle theorem is obtained for hybrid time-varying systems. Two examples are used to demonstrate the effectiveness of the results.