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distributed online optimization for multi-agent optimal transport

AUTOMATICA 2025年 171卷

作者： Krishnan, Vishaal Martinez, Sonia Harvard Univ Sch Engn & Appl Sci Cambridge MA 02138 USA Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

We propose a scalable, distributed algorithm for the optimal transport of large-scale multi-agent systems. We formulate the problem as one of steering the collective towards a target probability measure while minimizing the total cost of transport, with the additional constraint of distributed implementation. Using optimal transport theory, we realize the solution as an iterative transport based on a stochastic proximal descent scheme. At each stage of the transport, the agents implement an online, distributed primal-dual algorithm to obtain local estimates of the Kantorovich potential for optimal transport from the current distribution of the collective to the target distribution. Using these estimates as their local objective functions, the agents then implement the transport by stochastic proximal descent. This two-step process is carried out recursively by the agents to converge asymptotically to the target distribution. We rigorously establish the underlying theoretical framework and convergence of the algorithm and test its behavior in numerical experiments.

关键词： Optimal transport Stochastic optimization distributed online optimization Multi-agent systems

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distributed online optimization with Edge-Based Event-Triggered communication

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AUTOMATICA 2025年 173卷

作者： Mao, Shuai Mishra, Yateendra Tian, Yu-Chu Perc, Matjaz Tang, Yang Nantong Univ Sch Elect Engn Nantong 226019 Peoples R China Queensland Univ Technol Sch Comp Sci Brisbane Qld 4000 Australia Queensland Univ Technol Sch Elect Engn & Robot Brisbane Qld 4000 Australia Univ Maribor Fac Nat Sci & Math Koroska Cesta 160 Maribor 2000 Slovenia Complex Sci Hub Vienna Josefstadterstr 39 A-1080 Vienna Austria Kyung Hee Univ Dept Phys 26 Kyungheedae Ro Seoul 02447 South Korea East China Univ Sci & Technol Key Lab Smart Mfg Energy Chem Proc Minist Educ Shanghai 200237 Peoples R China

This study focuses on distributed online optimization (DOO) problems with and without constraints. It presents a discrete-time distributed method based on a push-sum protocol with Edge-Based Event-Triggered communications for DOO (EBET-DOO). In EBET-DOO, all agents operate within both unbalanced time-varying B-strongly connected topologies or unbalanced fixed strongly connected topologies due to the push-sum-based operation. They estimate and update time-varying optimal solutions in real time by using local objective functions and information from neighboring agents. Communication updates are governed by edge-based triggering conditions, reducing communication frequency compared to node-based event-triggered mechanisms. We demonstrate that, with specific triggered thresholds, EBET-DOO achieves sublinear growth rates for static regret (for both constrained and unconstrained optimization) and dynamic regret (for constrained optimization only), with orders root of O ((ln( T )) 2 ) and O ( T ), respectively. Simulation results in time-varying economic dispatch and online prediction for diabetes validate the efficacy of the proposed EBET-DOO. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： distributed online optimization Edge-based event-triggered mechanism Multi-agent system Sublinear regret

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distributed online optimization Under Dynamic Adaptive Quantization

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2024年第7期71卷 3453-3457页

作者： Zhou, Yingjie Wang, Xinyu Li, Tao East China Normal Univ Minist Educ Sch Math Sci Shanghai 200241 Peoples R China East China Normal Univ Minist Educ Key Lab Math & Engn Applicat Shanghai 200241 Peoples R China East China Normal Univ Sch Math Sci Shanghai 200241 Peoples R China Shenzhen Baimai Technol Co Ltd Algorithm Dept Shenzhen Peoples R China

For distributed online optimization over networked nodes, we propose an algorithm based on one-step gradient descent and multi-step consensus under dynamic adaptive quantization. We propose a dynamic difference encoding-decoding strategy with variable center quantizers and online-generated quantization intervals, which adjust the quantization parameters adaptively according to the optimizers' states. We use the fixed gradient descent step size to ensure the ability of tracking the optimal solutions of the dynamically changing objective functions, and give the upper bound of the dynamic regret. The effectiveness of the proposed algorithm is demonstrated by numerical simulation.

关键词： Heuristic algorithms Quantization (signal) optimization Linear programming Encoding Decoding Radio frequency distributed online optimization dynamic adaptive quantization finite dynamic difference coding

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distributed online optimization for integrated energy systems: A multi-agent system consensus approach

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2024年第10期38卷 3401-3421页

作者： Wang, Guofeng Liu, Yongqi Zhang, Youbing Yan, Jun Xie, Shuzong Zhejiang Univ Technol Coll Informat Engn Hangzhou Peoples R China Concordia Univ Gina Cody Sch Engn & Comp Sci Montreal PQ Canada Zhejiang Univ Sci & Technol Sch Automat & Elect Engn Hangzhou 310023 Peoples R China

The integration of multi-energy within distribution networks has escalated the need for efficient operation and control of integrated energy systems (IES). Addressing the complexities of real-time scheduling and low-carbon optimization, we propose a novel artificial intelligence driven multi-agent system (MAS) approach for modeling the interactions and operations within the multi-agent integrated energy systems (MA-IES) framework. In this framework, distinct components such as electric, gas, and heat networks are conceptualized as autonomous agents, each responsible for managing its domain while interacting with other agents to achieve system-wide efficiency and economical goals. The agents communicate and coordinate through a distributed online optimization framework, utilizing the alternating direction multiplier method (ADMM) to ensure effective consensus despite the inherent nontransparency of information exchange. This MAS based approach allows for dynamic adaptation of strategies based on local data and global objectives, significantly enhancing the responsiveness and adaptability of MA-IES. We further integrate an objective function reliant on a tiered carbon pricing mechanism to assess and minimize the environmental impact of operations. Enhanced by adaptive penalty coefficients within the ADMM, our MA-IES framework demonstrates improved convergence rates and robustness in operational scenarios. Empirical validation through detailed case studies confirms the superior performance of our MAS-based model, demonstrating its potential to realize an efficient and economical low-carbon operation of MA-IES.

关键词： adaptive penalty coefficient alternating direction method of multipliers (ADMM) distributed online optimization integrated energy systems (IES) multi-agent system (MAS) tiered carbon pricing mechanism

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distributed online optimization based on one-step gradient descent and multi-step consensus 18

Distributed online optimization based on one-step gradient d...

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18th International Conference on Control Automation Robotics and Vision

作者： Zhou, Yingjie Wang, Xinyu Li, Tao East China Normal Univ Sch Math Sci Shanghai 200241 Peoples R China Shenzhen Baimai Technol Co Ltd Shenzhen 518052 Peoples R China Minist Educ Key Lab Math & Engn Applicat Beijing Peoples R China

ISBN: (纸本)9798331518509;9798331518493

We propose a distributed online optimization algorithm with continuously learning ability. In this algorithm, we first perform one-step gradient descent with fixed step size to ensure the ability of tracking the optimal solutions, and then use multi-step consensus to ensure the collaboration between neighboring nodes. For strongly convex and smooth objective functions, we provide a dynamic regret analysis of the proposed algorithm and show that the dynamic regret is upper bounded by the initial values, the path variation of the optimal solution, and a linear growth term. The coefficient of the linear growth term can be made arbitrarily small by adjusting the step size of gradient descent. We also demonstrate the performance of the proposed algorithm by numerical simulations.

关键词： distributed online optimization dynamic regret continuously learning ability

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Differentially private distributed online optimization via push-sum one-point bandit dual averaging

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NEUROCOMPUTING 2024年 572卷

作者： Zhao, Zhongyuan Yang, Ju Gao, Wang Wang, Yan Wei, Mengli Nanjing Univ Informat Sci & Technol Jiangsu Key Lab Big Data Anal Technol Jiangsu Collaborat Innovat Ctr Atmospher Environm Coll Automat Nanjing 210044 Peoples R China Southeast Univ Sch Cyber Sci & Engn Nanjing 211189 Peoples R China

This paper focuses on the distributed online optimization problem in multi -agent systems considering privacy preservation. Each agent exchanges local information with neighboring agents on the strongly connected timevarying directed graphs. Since the process of information transmission is prone to information leakage, a distributed push -sum dual averaging algorithm based on the differential privacy mechanism is proposed to protect the privacy of the data. In addition, to handle situations where the gradient information of the node cost function is unknown, the one -point gradient estimation is designed to calculate the true gradient information and guide the update of the decision variables. With the appropriate choice of the stepsizes and the exploration parameters, the algorithm can effectively protect the privacy of agents while achieving sublinear regret with 3 the convergence rate O(T 4 ). Furthermore, this paper also explores the effect of one -point estimation parameters on the regret in the online setting and investigates the relation between the convergence effect of individual regret and differential privacy levels. Finally, several federated learning experiments were conducted to verify the efficacy of the algorithm.

关键词： distributed online optimization Differential privacy One-point gradient estimate Decentralized federated learning

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distributed online optimization subject to long-term constraints and time-varying topology: An event-triggered and bandit feedback approach

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2024年第16期361卷

作者： Zhang, Difeng Feng, Zhangcheng Xu, Wenying Yang, Shaofu Cao, Jinde Southeast Univ Sch Math Nanjing 211189 Jiangsu Provinc Peoples R China Southeast Univ Sch Comp Sci & Engn Nanjing 211189 Jiangsu Provinc Peoples R China

This paper considers the distributed online optimization problem (DOO) with long-term constraints (LTC) and bandit feedback under a time-varying communication network, where the cost functions are time-varying and only two specific values are disclosed to agents subsequent to their decision-making process. In order to alleviate computation and communication burdens, long-term constraints is considered, and an event-triggered strategy is established for scheduling network communication. Based on this, an event-triggered distributed online algorithm is proposed with two-point bandit feedback for the DOO-LTC through B-strongly connected communication. Two cases of general convex and strongly convex cost functions are taken into consideration. The derived upper bounds for the regret and cumulative absolute constraint violation (CACV) are O (T-max{c,T-1-c}) and O(T1-a/2) for a general convex cost function, and O(log T) and O(root T log T) for a strongly convex cost function, respectively. Finally, a numerical example of distributed online regularization linear regression is provided to show the effectiveness of the proposed algorithm.

关键词： distributed online optimization Long-term constraints Event-triggered strategy Bandit feedback

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distributed online optimization for Multi-Agent Networks With Coupled Inequality Constraints

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2021年第8期66卷 3575-3591页

作者： Li, Xiuxian Yi, Xinlei Xie, Lihua Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore KTH Royal Inst Technol ACCESS Linnaeus Ctr Elect Engn S-10044 Stockholm Sweden

This article investigates the distributed online optimization problem over a multi-agent network subject to local set constraints and coupled inequality constraints, which has a lot of applications in many areas, such as wireless sensor networks, power systems, and plug-in electric vehicles. In this problem, the cost function at each time step is the sum of local cost functions with each of them being gradually revealed to its corresponding agent, and meanwhile only local functions in coupled inequality constraints are accessible to each agent. To address this problem, a modified primal-dual algorithm, called distributed online primal-dual push-sum algorithm, is developed in this article, which does not rest on any assumption on parameter boundedness and is applicable to unbalanced networks. It is shown that the proposed algorithm is sublinear for both the dynamic regret and the violation of coupled inequality constraints. Finally, the theoretical results are supported by a simulation example.

关键词： Cost function Heuristic algorithms Vehicle dynamics Task analysis Standards Power systems Coupled inequality constraints distributed online optimization multi-agent networks primal-dual push-sum

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Push-Sum distributed online optimization With Bandit Feedback

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IEEE TRANSACTIONS ON CYBERNETICS 2022年第4期52卷 2263-2273页

作者： Wang, Cong Xu, Shengyuan Yuan, Deming Zhang, Baoyong Zhang, Zhengqiang Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Peoples R China Qufu Normal Univ Sch Elect Engn & Automat Rizhao 276826 Peoples R China

In this article, we concentrate on distributed online convex optimization problems over multiagent systems, where the communication between nodes is represented by a class of directed graphs that are time varying and uniformly strongly connected. This problem is in bandit feedback, in the sense that at each time only the cost function value at the committed point is revealed to each node. Then, nodes update their decisions by exchanging information with their neighbors only. To deal with Lipschitz continuous and strongly convex cost functions, a distributed online convex optimization algorithm that achieves sublinear individual regret for every node is developed. The algorithm is built on the algorithm called the push-sum scheme that releases the request of doubly stochastic weight matrices, and the one-point gradient estimator that requires the function value at only one point at every iteration, instead of the gradient information of loss function. The expected regret of our proposed algorithm scales as O(T-2/3 ln(2/3)(T)), and T is the number of iterations. To validate the performance of the algorithm developed in this article, we give a simulation of a common numerical example.

关键词： distributed online optimization multiagent systems one-point bandit feedback push-sum algorithm

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Privacy Masking Stochastic Subgradient-Push Algorithm for distributed online optimization

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IEEE TRANSACTIONS ON CYBERNETICS 2021年第6期51卷 3224-3237页

作者： Lu, Qingguo Liao, Xiaofeng Xiang, Tao Li, Huaqing Huang, Tingwen Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligen Chongqing 400715 Peoples R China Chongqing Univ Coll Comp Chongqing 400044 Peoples R China Texas A&M Univ Qatar Sci Program Doha Qatar

This article investigates the problem of distributed online optimization for a group of units communicating on time-varying unbalanced directed networks. The main target of the set of units is to cooperatively minimize the sum of all locally known convex cost functions (global cost function) while pursuing the privacy of their local cost functions being well masked. To address such optimization problems in a collaborative and distributed fashion, a differentially private-distributed stochastic subgradient-push algorithm, called DP-DSSP, is proposed, which ensures that units interact with in-neighbors and collectively optimize the global cost function. Unlike most of the existing distributed algorithms which do not consider privacy issues, DP-DSSP via differential privacy strategy successfully masks the privacy of participating units, which is more practical in applications involving sensitive messages, such as military affairs or medical treatment. An important feature of DP-DSSP is tackling distributed online optimization problems under the circumstance of time-varying unbalanced directed networks. Theoretical analysis indicates that DP-DSSP can effectively mask differential privacy as well as can achieve sublinear regrets. A compromise between the privacy levels and the accuracy of DP-DSSP is also revealed. Furthermore, DP-DSSP is capable of handling arbitrarily large but uniformly bounded delays in the communication links. Finally, simulation experiments confirm the practicability of DP-DSSP and the findings in this article.

关键词： Privacy Cost function Convex functions Delays Stochastic processes Communication delays differential privacy distributed online optimization stochastic subgradient-push algorithm time-varying directed networks

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