This paper studies state quantization schemes for feedback stabilization of control systems with limited information. The focus is on designing the least destabilizing quantizer subject to a given information constraint. We explore several ways of measuring the destabilizing effect of a quantizer on the closed-loop system, including (but not limited to) the worst-case quantization error. In each case, we show how quantizer design can be naturally reduced to a version of the so-called multicenter problem from locational optimization. Algorithms for solving such problems are discussed. In particular, an iterative solver is developed for a novel weighted multicenter problem which most accurately represents the least destabilizing quantizer design.
We study the interdependence between transportation and power systems considering decentralized renewable generators and electric vehicles (EVs). We formulate the problem in a stochastic multi-agent optimization framework considering the complex interactions between EV/conventional vehicle drivers, \revi{renewable}/conventional generators, and independent system operators, with locational electricity and charging prices endogenously determined by markets. We show that the multi-agent optimization problems can be reformulated as a single convex optimization problem and prove the existence and u…
This paper studies the network optimization problem about which a group of agents cooperates to minimize a global function under practical constraints of finite bandwidth communication. Particularly, we propose an adaptive encoding-decoding scheme to handle the constrained communication between agents. Based on this scheme, the continuous-time quantized distributed primal-dual (QDPD) algorithm is developed for network optimization problems. We prove that our algorithms can exactly track an optimal solution to the corresponding convex global cost function at a linear convergence rate. Furthermo…
Multi-agent distributed optimization over a network minimizes a global objective formed by a sum of local convex functions using only local computation and communication. We develop and analyze a quantized distributed algorithm based on the alternating direction method of multipliers (ADMM) when inter-agent communications are subject to finite capacity and other practical constraints. While existing quantized ADMM approaches only work for quadratic local objectives, the proposed algorithm can deal with more general objective functions (possibly non-smooth) including the LASSO. Under certain co…
Communication efficiency is a major bottleneck in the applications of distributed networks. To address the problem, the problem of quantized distributed optimization has attracted a lot of attention. However, most of the existing quantized distributed optimization algorithms can only converge sublinearly. To achieve linear convergence, this paper proposes a novel quantized distributed gradient tracking algorithm (Q-DGT) to minimize a finite sum of local objective functions over directed networks. Moreover, we explicitly derive the update rule for the number of quantization levels, and prove th…
Regularized coordinate minimization for nonconvex composite optimization with application to quantized image compression
Politehnica Bucharest（布加勒斯特理工大学）；Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy（罗马尼亚科学院格奥尔基·米霍克-卡尤斯·雅各布数学统计与应用数学研究所）
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a novel linear programming approach, which is effective to tackle this problem. In particular, we prove theoretical guarantees of robustness, and we present numerical results that show improved performance with respect to the state-of-the-art methods.
Decentralized Linearized Consensus ADMM with Efficient Quantized Communication
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（瑞典皇家理工学院）
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…
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）
RIKEN Center for Advanced Intelligence Project (AIP)（理化学研究所先进智能项目中心）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；Artificial Intelligence Research Institute (AIRI)（人工智能研究院）
We present a novel procedure for optimization based on the combination of efficient quantized tensor train representation and a generalized maximum matrix volume principle. We demonstrate the applicability of the new Tensor Train Optimizer (TTOpt) method for various tasks, ranging from minimization of multidimensional functions to reinforcement learning. Our algorithm compares favorably to popular evolutionary-based methods and outperforms them by the number of function evaluations or execution time, often by a significant margin.
We investigate fast and communication-efficient algorithms for the classic problem of minimizing a sum of strongly convex and smooth functions that are distributed among $n$ different nodes, which can communicate using a limited number of bits. Most previous communication-efficient approaches for this problem are limited to first-order optimization, and therefore have \emph{linear} dependence on the condition number in their communication complexity. We show that this dependence is not inherent: communication-efficient methods can in fact have sublinear dependence on the condition number. For …
Yale University（耶鲁大学）；Massachusetts Institute of Technology（麻省理工学院）；University of Pennsylvania（宾夕法尼亚大学）
How can we efficiently mitigate the overhead of gradient communications in distributed optimization? This problem is at the heart of training scalable machine learning models and has been mainly studied in the unconstrained setting. In this paper, we propose Quantized-Frank-Wolfe (QFW), the first projection-free and communication-efficient algorithm for solving constrained optimization problems at scale. We consider both convex and non-convex objective functions, expressed as a finite-sum or more generally a stochastic optimization problem, and provide strong theoretical guarantees on the conv…
Distributed Optimization with Nesterov Momentum and Finite-Time Quantized Consensus
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）
A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference $f=g-h$ of two convex functions $g$ and $h$. In particular, we deal with the special case where one of the two convex functions $g$ or $h$ is polyhedral. In case $g$ is polyhedral, we show that a solution of the DC program can be obtained from a solution of an associated polyhedral projection problem. In case $h$ is polyhedral, we prove that a solution of the DC program can be obtained by solving a polyhedral projection problem and finitely many convex pr…
Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking
National Special Education Resource Center for Children with Autism, Zhejiang Normal University（浙江师范大学生自闭症教育资源中心）；School of Computer Science and Technology, Zhejiang Normal University（浙江师范大学计算机科学与技术学院）；China Mobile Research Institute（中国移动研究院）；Institute of Cyber-Systems and Control, Zhejiang University（浙江大学控制系统研究所）；SGIT AI Lab, State Grid Corporation of China（国网SGIT人工智能实验室）；Zhejiang Key Laboratory of Intelligent Education Technology and Application, Zhejiang Normal University（浙江智能教育技术与应用重点实验室）；School of Information Engineering, Huzhou University（湖州大学信息工程学院）；Centre for Frontier Artificial Intelligence Research, A*STAR（A*STAR前沿人工智能研究中心）
IITB-Monash Research Academy（IITB-莫纳什研究学院）；Indian Institute of Technology Bombay（印度理工学院孟买分校）；Monash University（莫纳什大学）
This paper is concerned with the deployment of multiple mobile robots in order to autonomously cover a region Q. The region to be covered is described using a density function which may not be apriori known. In this paper, we pose the coverage problem as an optimization problem over some space of functions on Q. In particular, we look at L 2 -distance based coverage algorithm and derive adaptive control laws for the same. We also propose a modified adaptive control law incorporating consensus for better parameter convergence. We implement the algorithms on real differential drive robots with b…
University of California, Santa Barbara（加州大学圣巴巴拉分校）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；University of Pennsylvania（宾夕法尼亚大学）
We consider the problem of decentralized consensus optimization, where the sum of $n$ smooth and strongly convex functions are minimized over $n$ distributed agents that form a connected network. In particular, we consider the case that the communicated local decision variables among nodes are quantized in order to alleviate the communication bottleneck in distributed optimization. We propose the Quantized Decentralized Gradient Descent (QDGD) algorithm, in which nodes update their local decision variables by combining the quantized information received from their neighbors with their local in…
We consider the problem of deep neural net compression by quantization: given a large, reference net, we want to quantize its real-valued weights using a codebook with $K$ entries so that the training loss of the quantized net is minimal. The codebook can be optimally learned jointly with the net, or fixed, as for binarization or ternarization approaches. Previous work has quantized the weights of the reference net, or incorporated rounding operations in the backpropagation algorithm, but this has no guarantee of converging to a loss-optimal, quantized net. We describe a new approach based on …
Due to its efficiency and ease to implement, stochastic gradient descent (SGD) has been widely used in machine learning. In particular, SGD is one of the most popular optimization methods for distributed learning. Recently, quantized SGD (QSGD), which adopts quantization to reduce the communication cost in SGD-based distributed learning, has attracted much attention. Although several QSGD methods have been proposed, some of them are heuristic without theoretical guarantee, and others have high quantization variance which makes the convergence become slow. In this paper, we propose a new method…
Quantized constant envelope (QCE) precoding, a new transmission scheme that only discrete QCE transmit signals are allowed at each antenna, has gained growing research interests due to its ability of reducing the hardware cost and the energy consumption of massive multiple-input multiple-output (MIMO) systems. However, the discrete nature of QCE transmit signals greatly complicates the precoding design. In this paper, we consider the QCE precoding problem for a massive MIMO system with phase shift keying (PSK) modulation and develop an efficient approach for solving the constructive interferen…
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…
