We propose two distributed iterative algorithms that can be used to solve, in finite time, the distributed optimization problem over quadratic local cost functions in large-scale networks. The first algorithm exhibits synchronous operation whereas the second one exhibits asynchronous operation. Both algorithms share salient features. Specifically, the algorithms operate exclusively with quantized values, which means that the information stored, processed and exchanged between neighboring nodes is subject to deterministic uniform quantization. The algorithms rely on event-driven updates in order to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage. Finally, once the algorithms converge, nodes distributively terminate their operation. We prove that our algorithms converge in a finite number of iterations to the exact optimal solution depending on the quantization level, and we present applications of our algorithms to (i) optimal task scheduling for data centers, and (ii) global model aggregation for distributed federated learning. We provide simulations of these applications to illustrate the operation, performance, and advantages of the proposed algorithms. Additionally, it is shown that our proposed algorithms compare favorably to algorithms in the current literature. Quantized communication and asynchronous updates increase the required time to completion, but finite-time operation is maintained.
We study the distributed average consensus problem in multi-agent systems with directed communication links that are subject to quantized information flow. The goal of distributed average consensus is for the nodes, each associated with some initial value, to obtain the average (or some value close to the average) of these initial values. In this paper, we present and analyze a distributed averaging algorithm which operates exclusively with quantized values (specifically, the information stored, processed and exchanged between neighboring agents is subject to deterministic uniform quantization…
We consider the problems of computing the average degree and the size of a given network in a distributed fashion under quantized communication. We present two distributed algorithms which rely on quantized operation (i.e., nodes process and transmit quantized messages), and are able to calculate the exact solutions in a finite number of steps. Furthermore, during the operation of our algorithms, each node is able to determine in a distributed manner whether convergence has been achieved and thus terminate its operation. To the best of the authors' knowledge these algorithms are the first to f…
Affine-coupled Distributed Optimization via Distributed Proximal Jacobian ADMM with Quantized Communication
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；University of Bologna（博洛尼亚大学）；KTH Royal Institute of Technology（皇家理工学院）；The Hong Kong University of Science and Technology（香港科技大学）
We study the distributed average consensus problem in multi-agent systems with directed communication links that are subject to quantized information flow. The goal of distributed average consensus is for the nodes, each associated with some initial value, to obtain the average (or some value close to the average) of these initial values. In this paper, we present and analyze novel distributed averaging algorithms which operate exclusively on quantized values (specifically, the information stored, processed and exchanged between neighboring agents is subject to deterministic uniform quantizati…
This paper considers a distributed optimization problem in a multi-agent system where a fraction of the agents act in an adversarial manner. Specifically, the malicious agents steer the network of agents away from the optimal solution by sending false information to their neighbors and consume significant bandwidth in the communication process. We propose a distributed gradient-based optimization algorithm in which the non-malicious agents exchange quantized information with one another. We prove convergence of the solution to a neighborhood of the optimal solution, and characterize the soluti…
In this paper, we present a distributed algorithm which implements the $k$-means algorithm in a distributed fashion for multi-agent systems with directed communication links. The goal of $k$-means is to partition the network's agents in mutually exclusive sets (groups) such that agents in the same set have (and possibly share) similar information and are able to calculate a representative value for their group.During the operation of our distributed algorithm, each node (i) transmits quantized values in an event-driven fashion, and (ii) exhibits distributed stopping capabilities. Transmitting …
This paper considers the distributed filtering problem for a class of stochastic uncertain systems under quantized data flowing over switching sensor networks. Employing the biased noisy observations of the local sensor and interval-quantized messages from neighboring sensors successively, an extended state based distributed Kalman filter (DKF) is proposed for simultaneously estimating both system state and uncertain dynamics. To alleviate the effect of observation biases, an event-triggered update based DKF is presented with a tighter mean square error bound than that of the time-driven one b…
In networked control systems, often the sensory signals are quantized before being transmitted to the controller. Consequently, performance is affected by the coarseness of this quantization process. Modern communication technologies allow users to obtain resolution-varying quantized measurements based on the prices paid. In this paper, we consider joint optimal controller synthesis and quantizer scheduling for a partially observed Quantized-Feedback Linear-Quadratic-Gaussian (QF-LQG) system, where the measurements are quantized before being sent to the controller. The system is presented with…
In this paper, we analyze the problem of optimally allocating resources in a distributed and privacy-preserving manner. We propose a novel distributed optimal resource allocation algorithm with privacy-preserving guarantees, which operates over a directed communication network. Our algorithm converges in finite time and allows each node to process and transmit quantized messages. Our algorithm utilizes a distributed quantized average consensus strategy combined with a privacy-preserving mechanism. We show that the algorithm converges in finite-time, and we prove that, under specific conditions…
Distributed Optimization with Nesterov Momentum and Finite-Time Quantized Averaging over Directed Networks: Extended Version
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；KTH Royal Institute of Technology（皇家理工学院）
In networked control systems, often the sensory signals are quantized before being transmitted to the controller. Consequently, performance is affected by the coarseness of this quantization process. Modern communication technologies allow users to obtain resolution-varying quantized measurements based on the prices paid. In this paper, we consider optimal controller synthesis of a Quantized-Feedback Linear-Quadratic-Gaussian (QF-LQG) system where the measurements are to be quantized before being transmitted to the controller. The system is presented with several choices of quantizers, along w…
In this paper, we consider the problem of privacy preservation in the average consensus problem when communication among nodes is quantized. More specifically, we consider a setting where some nodes in the network are curious but not malicious and they try to identify the initial states of other nodes based on the data they receive during their operation (without interfering in the computation in any other way), while some nodes in the network want to ensure that their initial states cannot be inferred exactly by the curious nodes. We propose two privacy-preserving event-triggered quantized av…
An optimal control law for networked control systems with a discrete-time linear time-invariant (LTI) system as plant and networks between sensor and controller as well as between controller and actuator is proposed. This controller is designed by solving an optimization problem that is a generalization of the optimization problem used to obtain the Linear Quadratic Regulator (LQR) for deterministic discrete-time LTI systems. The networks are represented by random delays and drop outs of transmitted data packets.
Controlling network systems has become a problem of paramount importance. In this paper, we consider a distributed linear-quadratic problem and propose the use of graph neural networks (GNNs) to parametrize and design a distributed controller for network systems. GNNs exhibit many desirable properties, such as being naturally distributed and scalable. We cast the distributed linear-quadratic problem as a self-supervised learning problem, which is then used to train the GNN-based controllers. We also obtain sufficient conditions for the resulting closed-loop system to be input-state stable, and…
The linear-quadratic controller is one of the fundamental problems in control theory. The optimal solution is a linear controller that requires access to the state of the entire system at any given time. When considering a network system, this renders the optimal controller a centralized one. The interconnected nature of a network system often demands a distributed controller, where different components of the system are controlled based only on local information. Unlike the classical centralized case, obtaining the optimal distributed controller is usually an intractable problem. Thus, we ado…
In this paper we study the distributed average consensus problem in multi-agent systems with directed communication links that are subject to quantized information flow. Specifically, we present and analyze a distributed averaging algorithm which operates exclusively with quantized values (i.e., the information stored, processed and exchanged between neighboring agents is subject to deterministic uniform quantization) and relies on event-driven updates (e.g., to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage). The main idea of the proposed algori…
Aalto University（阿尔托大学）；Semnan University（塞姆南大学）；University of Cyprus（塞浦路斯大学）；Georgia State University（佐治亚州立大学）；University of Waterloo（滑铁卢大学）；City University of Hong Kong（香港城市大学）；Tufts University（塔夫茨大学）
This paper proposes networked dynamics to solve resource allocation problems over time-varying multi-agent networks. The state of each agent represents the amount of used resources (or produced utilities) while the total amount of resources is fixed. The idea is to optimally allocate the resources among the group of agents by minimizing the overall cost function subject to fixed sum of resources. Each agents' information is restricted to its own state and cost function and those of its immediate in-neighbors. This is motivated by distributed applications such as mobile edge-computing, economic…
Distributed Coordination Algorithms with Efficient Communication for Open Multi-Agent Systems with Dynamic Communication Links and Processing Delays: Extended Version
Composed of spatially distributed sensors and actuators that communicate through wireless networks, networked control systems are emerging as a fundamental infrastructure technology in 5G and IoT technologies, including diverse applications, such as autonomous vehicles, UAVs, and various sensing devices. In order to increase flexibility and reduce deployment and maintenance costs, many such applications consider battery-powered or energy-harvesting networks, which bring additional limitations on the energy consumption of the wireless network. Specifically, the operation of battery-powered or e…
Purdue University（普渡大学）；Sandia National Laboratories（桑迪亚国家实验室）
We consider the problem of distributed inference where agents in a network observe a stream of private signals generated by an unknown state, and aim to uniquely identify this state from a finite set of hypotheses. We focus on scenarios where communication between agents is costly, and takes place over channels with finite bandwidth. To reduce the frequency of communication, we develop a novel event-triggered distributed learning rule that is based on the principle of diffusing low beliefs on each false hypothesis. Building on this principle, we design a trigger condition under which an agent …
Classical linear quadratic (LQ) control centers around linear time-invariant (LTI) systems, where the control-state pairs introduce a quadratic cost with time-invariant parameters. Recent advancement in online optimization and control has provided novel tools to study LQ problems that are robust to time-varying cost parameters. Inspired by this line of research, we study the distributed online LQ problem for identical LTI systems. Consider a multi-agent network where each agent is modeled as an LTI system. The LTI systems are associated with decoupled, time-varying quadratic costs that are rev…
In this paper we consider a recently developed distributed optimization algorithm based on gradient tracking. We propose a system theory framework to analyze its structural properties on a preliminary, quadratic optimization set-up. Specifically, we focus on a scenario in which agents in a static network want to cooperatively minimize the sum of quadratic cost functions. We show that the gradient tracking distributed algorithm for the investigated program can be viewed as a sparse closed-loop linear system in which the dynamic state-feedback controller includes consensus matrices and optimizat…
Linear-Quadratic Gaussian Games with Distributed Sparse Estimation
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Oden Institute for Computational Engineering and Sciences（奥登计算工程与科学学院）；DEVCOM Army Research Laboratory（美军研究开发司令部陆军研究实验室）
We study the self-triggered stabilization of discrete-time linear systems with quantized state measurements. In the networked control system we consider, sensors may be spatially distributed and be connected to a self-triggering mechanism through finite data-rate channels. Each sensor independently encodes its measurements and sends them to the self-triggering mechanism. The self-triggering mechanism integrates quantized measurement data and then computes sampling times. Assuming that the closed-loop system is stable in the absence of quantization and self-triggered sampling, we propose a join…
We study the distributed Linear Quadratic Gaussian (LQG) control problem in discrete-time and finite-horizon, where the controller depends linearly on the history of the outputs and it is required to lie in a given subspace, e.g. to possess a certain sparsity pattern. It is well-known that this problem can be solved with convex programming within the Youla domain if and only if a condition known as Quadratic Invariance (QI) holds. In this paper, we first show that given QI sparsity constraints, one can directly descend the gradient of the cost function within the domain of output-feedback cont…
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）
This paper considers a distributed reinforcement learning problem for decentralized linear quadratic control with partial state observations and local costs. We propose a Zero-Order Distributed Policy Optimization algorithm (ZODPO) that learns linear local controllers in a distributed fashion, leveraging the ideas of policy gradient, zero-order optimization and consensus algorithms. In ZODPO, each agent estimates the global cost by consensus, and then conducts local policy gradient in parallel based on zero-order gradient estimation. ZODPO only requires limited communication and storage even i…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the convergence rate of MD in centralized and distributed settings under both strongly convex and non-strongly convex assumptions. We view MD with a dynamical system lens and leverage quadratic constraints (QCs) to provide explicit convergence rates based on Lyapunov stability. For centralized MD under strongly convex assumption, we develop a SDP that certifies exponent…
KTH Royal Institute of Technology（瑞典皇家理工学院）；School of Electrical Engineering and Computer Science, and Digital Futures, KTH Royal Institute of Technology（电气工程和计算机科学与数字未来学院，瑞典皇家理工学院）
In this paper, a cooperative Linear Quadratic Regulator (LQR) problem is investigated for multi-input systems, where each input is generated by an agent in a network. The input matrices are different and locally possessed by the corresponding agents respectively, which can be regarded as different ways for agents to control the multi-input system. By embedding a fully distributed information fusion strategy, a novel cooperative LQR-based controller is proposed. Each agent only needs to communicate with its neighbors, rather than sharing information globally in a network. Moreover, only the joi…
Near-Optimal Distributed Linear-Quadratic Regulator for Networked Systems
Mathematics and Computer Science Division, Argonne National Laboratory（阿贡国家实验室数学与计算机科学部）；California Institute of Technology（加州理工学院）；Department of Electrical and Computer Engineering, Carnegie Mellon University（卡内基梅隆大学电气与计算机工程系）；Department of Statistics, University of Chicago（芝加哥大学统计系）
