Distributed Learning Over Networks: Effect of Using Historical Observations

Communication-efficient distributed cubic Newton with compressed lazy Hessian

In learning systems, high operation precision is often a desirable objective for the algorithm design. Though centralized algorithms are generally adopted, they are subjected to restrictive hypotheses on the learning systems. To overcome this challenging problem, we aim to propose some distributed learning algorithms that focus specifically on achieving the perfect tracking tasks for iterative learning control (ILC) systems. By noting the equivalent relation between the perfect tracking problem of ILC systems and the solving problem of linear algebraic equations (LAEs), we first present an observer-based distributed learning algorithm to solve LAEs, where a multiagent system is constructed with every agent being only required to access some partial information for LAEs. The distributed learning algorithm benefits from integrating both observer-based design and consensus-based design ideas such that for any solvable LAE, all agents can agree on a common solution of it under any initial conditions of agents, regardless of whether it has a unique solution or not. Then, with the distributed learning algorithm for LAEs, we further develop two classes of distributed learning control algorithms for ILC systems, which establish the perfect tracking objective in the presence of the trackable desired output even without using the basic relative degree condition that is generally imposed for conventional ILC.

In the context of global energy transition, China's power industry is facing the challenge of green and low carbon transformation, and it is necessary to optimize the power supply strategy to cope with the problem of power surplus and consumption. The dynamic change of power load demand makes the traditional on-demand generation mode difficult to continue. Among data-driven load forecasting technologies, Gated Recurrent Unit (GRU) has potential application in the field of load forecasting due to its advantages, but data dispersion and privacy issues restrict the performance improvement of the model. As an emerging machine learning paradigm, distributed learning can realize multi-party collaborative training model, protect data privacy and integrate the advantages of multi-source data. Based on the distributed learning framework and the advantages of time series modeling of GRU network, this paper proposes a load forecasting method for photovoltaic system. A distributed learning algorithm is designed to realize efficient collaboration of multiple participants, and the GRU model parameters are optimized by linear aggregation, which provides strong support for optimal scheduling and stable operation of power system.

Consensus conditions and convergence speeds are crucial for distributed consensus algorithms of networked systems. Based on a basic first-order average-consensus protocol with time-varying topologies and additive noises, this paper first investigates its critical consensus condition on network topology by stochastic approximation frameworks. A new joint-connectivity condition called extensible joint-connectivity that contains a parameter $\delta$ (termed the extensible exponent) is proposed. With this and a balanced topology condition, we show that a critical value of $\delta$ for consensus is $1/2$ . Optimization on convergence rate of this protocol is further investigated. It is proved that the fastest convergence rate, which is the theoretic optimal rate among all controls, is of the order $1/t$ for the best topologies, and is of the order $1/t^{1-2\delta }$ for the worst topologies, which are balanced and satisfy the extensible joint-connectivity condition. For practical implementation, certain open-loop control strategies are introduced to achieve consensus with a convergence rate of the same order as the fastest convergence rate. Furthermore, a consensus condition is derived for nonstationary and strongly correlated random topologies. The algorithms and consensus conditions are applied to distributed consensus computation of mobile ad-hoc networks; and their related critical exponents are derived from relative velocities of mobile agents for guaranteeing consensus.

Motivated by applications of distributed linear estimation, distributed control, and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically, our interest is in designing such an algorithm with the fastest rate of convergence given the topological constraints of the network. As the main result of this paper, we design an algorithm with the fastest possible rate of convergence using a nonreversible Markov chain on the given network graph. We construct such a Markov chain by transforming the standard Markov chain, which is obtained using the Metropolis-Hastings method. We call this novel transformation <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pseudo-lifting</i> . We apply our method to graphs with geometry, or graphs with doubling dimension. Specifically, the convergence time of our algorithm (equivalently, the mixing time of our Markov chain) is proportional to the diameter of the network graph and hence optimal. As a byproduct, our result provides the fastest mixing Markov chain given the network topological constraints, and should naturally find their applications in the context of distributed optimization, estimation and control.

This study aims to provide a robust trajectory tracking controller which guarantees the prescribed performance of a robot manipulator, both in transient and steady-state modes, experiencing parametric uncertainties. The main core of the controller is designed based on the adaptive finite-time sliding mode control (SMC) and extreme learning machine (ELM) methods to collectively estimate the parametric model uncertainties and enhance the quality of tracking performance. Accordingly, the global estimation with a fast convergence rate is achieved while the tracking error and the impact of chattering on the control input are mitigated significantly. Following the control design, the stability of the overall control system along with the finite-time convergence rate is proved, and the effectiveness of the proposed method is investigated via extensive simulation studies. The results of simulations confirm that the prescribed transient and steady-state performances are obtained with enough accuracy, fast convergence rate, robustness, and smooth control input which are all required for practical implementation and applications.

Analyzing massive amounts of data using complex machine learning models requires significant computational resources. The conventional approach to such problems involves centralizing training data and inference processes in the cloud, i.e., in data centers. However, with the proliferation of mobile devices and increasing application of the Internet-of-Things (IoT) paradigm, very large amounts of data are collected at the edges of wireless networks, and due to privacy constraints and limited communication resources, it is undesirable or impractical to upload this data from mobile devices to the cloud for centralized learning. This problem can be solved by distributed learning at the network edge, by which edge devices collaboratively train a shared learning model using real-time mobile data. The avoidance of raw-data uploading not only helps to preserve privacy but may also alleviate network-traffic congestion and minimize latency. With that said, distributed training still requires a substantial amount of information exchange between devices and edge servers over wireless links. In the process, wireless impairments such as noise, interference, and imperfect knowledge of channel states can significantly slow down distributed learning (e.g., convergence speed) and degrades its performance (e.g., learning accuracy). This makes it crucial to optimize wireless network performance so as to support the efficient deployment of distributed learning algorithms. On the other hand, distributed learning algorithms provide a powerful tool-set for solving complex problems in wireless communication and networking. One important framework, called federated learning (FL), enables users to collaboratively learn a shared model while helping to preserve local data privacy. The application of FL can endow edge devices with capabilities of user behavior prediction, user identification, and wireless environment analysis. As another example, distributed reinforcement learning is capable of leveraging distributed computation power and data to solve complex optimization and control problems that arise in various use cases, such as network control, user clustering, resource management, and interference alignment. To cover this paradigm of distributed learning over wireless networks, this two-part Special Issue features papers dealing with two main research challenges: a) optimization of wireless network performance for efficient implementation of distributed learning in wireless networks, and b) distributed learning for solving communication problems and optimizing network performance.

Cardiomyopathy refers to gradual weakening of the muscular walls of the cardiac chambers. Due to the hypertrophic condition of the muscular walls, damage and stretching of the muscle may lead to arrhythmias, which is detectable using the ECG. In the past, any deviations from a healthy rhythm provide cardiologists with accurate information regarding the heart condition. However, cardiologists are prone to making inaccurate interpretation from the visual observation, leading to erroneous diagnosis. Hence, this paper proposes a computerized method for accurate analysis and detection of cardiomyopathy disease using MLP network. Data for normal, cardiomyopathy, and other arrhythmias were obtained from the PTB Diagnostic ECG database. The raw signals were preprocessed for high-frequency noise removal using median and moving average filters. Baseline corrections were conducted using two-stage polynomial fitting method. Nine time-based features were extracted from the three bipolar limb leads. A total of 600 beats were used to train, validate and test five different MLP network structures. Four different learning algorithms were implemented to obtain the best classification accuracy and fastest convergence rate. Results show that the Levenberg-Marquardt algorithm shows the highest average classification accuracy of 98.9% for the different structures with the fastest average convergence rate of 12 epochs.

This paper investigates the optimal synchronisation problem for unknown nonlinear heterogeneous multi-agent systems (MASs) with an active leader and disturbances. Due to the external input signal of the active leader, the resulted uncooperative behaviours and unpredictability increase difficulty to derive the analytical solution of the coupled Bellman equation. To this end, we develop a distributed model reference adaptive critic learning algorithm with a hierarchical and distributed synchronisation control framework, which transforms the synchronisation problem of unknown nonlinear MASs into that of defined reference ones. Moreover, the algorithm extends our previous work to the distributed MASs, so that it is guaranteed that all the agents reach an agreement with the minimised transient errors and robustness against the disturbances and the neural network (NN) approximation errors. It is proved that the local neighbour tracking errors and the NN weight estimation errors are uniformly ultimately bounded via Lyapunov stability theory. A simulation example for multi-manipulator systems demonstrates the effectiveness of the algorithm.

Traditional equalization algorithms for multiple input multiple output (MIMO) systems suffer from high complexity and low convergence rate. So an improved adaptive reduced-rank joint detection algorithm of multistage Wiener filter (MSWF) based on rectangle blocking matrices is proposed. The MSWF is implemented by the correlation subtraction algorithm (CSA) structure and is called unitary multistage Wiener filter (UMSWF). The new scheme adopts rectangle submatrix as blocking matrix, which is chosen from the square blocking matrix for UMSWF. The proposed algorithm can reduce the size of the observation data vectors step by step in the forward recursion decomposition of UMSWF. Thus, the computational complexity is reduced and the convergence rate is increased. Theoretical analysis and simulation results show that this improved adaptive reduced-rank joint detection algorithm of UMSWF based on rectangle blocking matrix has better performance such as lower complexity and faster convergence rate. In particular, simulations are conducted in the vertical-Bell Labs layered space-time (V-BLAST) system which adopts BPSK modulation, where 4 and 8 antennas are equipped at the transmitter and receiver, respectively. Compared with traditional equalization algorithm based on UMSWF, our new method can achieve the same BER performance at high SNR with only 0.5 times that of computational complexity.

This paper gives a theoretical analysis of high-dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis the poor performances of standard procedures in the case when dimension p is larger than sample size n. The corresponding theoretical results are non-asymptotic lower bounds. On the other hand, we propose two discrimination procedures based on dimensionality reduction and provide associated rates of convergence which can be O(log(p)/n) under sparsity assumptions. Finally, all our results rely on a theorem that provides simple sharp relations between the excess risk and an estimation error associated with the geometric parameters defining the used discrimination rule.

In this paper, we present new methods for black-box convex minimization. They do not need to know in advance the actual level of smoothness of the objective function. Their only essential input parameter is the required accuracy of the solution. At the same time, for each particular problem class they automatically ensure the best possible rate of convergence. We confirm our theoretical results by encouraging numerical experiments, which demonstrate that the fast rate of convergence, typical for the smooth optimization problems, sometimes can be achieved even on nonsmooth problem instances.

Noise and interference are the two most common and basic problems in wireless communication systems. The noise in wireless communication channels has the characteristics of randomness and impulsivity, so the performance of adaptive filtering algorithms based on geometric algebra (GA) and second-order statistics is greatly reduced in the wireless communication systems. In order to improve the performance of adaptive filtering algorithms in wireless communication systems, this paper proposes two novel GA-based adaptive filtering algorithms, which are deduced from the robust algorithms based on the minimum error entropy (MEE) criterion and the joint criterion (MSEMEE) of the MEE and the mean square error (MSE) with the help of GA theory. The noise interference in wireless communication is modeled by alpha-stable distribution which is in good agreement with the actual data in this paper. Simulation results show that for the mean square deviation (MSD) learning curve, the GA-based MEE (GA-MEE) algorithm has faster convergence rate and better steady-state accuracy compared to the GA-based maximum correntropy criterion algorithm (GA-MCC) under the same generalized signal-to-noise ratio (GSNR). The GA-MEE algorithm reduces the convergence rate, but improves the steady-state accuracy by 10–15 dB compared to the adaptive filtering algorithms based on GA and second-order statistics. For GA-based MSEMEE (GA-MSEMEE) algorithm, when GA-MSEMEE and the adaptive filtering algorithms based on GA and second-order statistics keep the same convergence rate, its steady-state accuracy is improved by 10–15 dB, and when GA-MSEMEE and GA-MEE maintain approximately steady-state accuracy, its convergence rate is improved by nearly 100 iterations. In addition, when the algorithms are applied to noise cancellation, the average recovery error of the two proposed algorithms is 7 points lower than that of other GA-based adaptive filtering algorithms. The results validate the effectiveness and superiority of the GA-MEE and GA-MSEMEE algorithms in the alpha-stable noise environment, providing new methods to deal with multi-channel interference in wireless networks.

In this paper, we build bounded error observers for a common class of partially known bioreactor models. The main idea is to construct hybrid bounded observers "between" high gain observer, which has an adjustable convergence rate but requires perfect knowledge of the model, and asymptotic observer which is very robust towards uncertainty but has a fixed convergence rate. An hybrid bounded error observer which reconstructs the two state variables is constructed considering two steps: first step is similar to a high gain observer meaning that fast convergence rate but error depending on the knowledge of the model are obtained; second step is a switch to an observer similar to the asymptotic one meaning that fixed convergence rate towards an error as small as desired is obtained. Thus, a better convergence rate of estimated variables than the classical asymptotic observer is obtained.

The capacitated arc routing problem (CARP) is a classical NP-Hard combinatorial optimization problem. In this paper, we present a memetic algorithm based on Extension step and Statistical filtering for Large-Scale CARP (ESMAENS) which has improvements in both the global search strategy and the local search strategy. Firstly, ESMAENS adopts the Route Distance Grouping decomposition scheme (RDG) to decompose the large-scale CARP into some independent sub-problems. Then, the initial population would evolve into a new group by using the Evolutionary Algorithm. Furthermore, ESMAENS introduces the extension step search strategy to search the potential solutions around the current solution. As a result, with the increase of the iteration number, it avoids getting to the premature convergence. Meanwhile, the diversity of the population can be increased. Finally, in the local search strategy, the statistical filter is used to filter out some solutions and make the algorithm get the lower bound at a faster convergence rate with a high stability. Compared with RDG-MAENS, experimental results on Beullen’C, D, E, F, egl and EGL-G test set show that ESMAENS has a better convergence rate, and the stability of solutions obtained is improved. Furthermore, ESMAENS achieves a global search for the solutions. Especially for the large-scale EGL-G test set, ESMAENS can converge to a lower bound at a faster convergence rate, and it is suitable for solving large-scale CARP.