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Distributed Online Convex Optimization with Time-Varying Constraints: Tighter Cumulative Constraint Violation Bounds under Slater's Condition

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IEEE Transactions on Automatic control 2025年

作者： Yi, Xinlei Li, Xiuxian Yang, Tao Xie, Lihua Hong, Yiguang Chai, Tianyou Johansson, Karl H. National Key Laboratory of Autonomous Intelligent Unmanned Systems Shanghai Institute of Intelligent Science and Technology China Ministry of Education Frontiers Science Center for Intelligent Autonomous Systems China Massachusetts Institute of Technology Lab for Information & Decision Systems CambridgeMA02139 United States Northeastern University State Key Laboratory of Synthetical Automation for Process Industries Shenyang110819 China Nanyang Technological University School of Electrical and Electronic Engineering 50 Nanyang Avenue 639798 Singapore Kth Royal Institute of Technology Division of Decision and Control Systems School of Electrical Engineering and Computer Science Sweden Digital Futures Stockholm10044 Sweden

This paper considers distributed online convex optimization with time-varying constraints. In this setting, a network of agents makes decisions at each round, and then only a portion of the loss function and a coordinate block of the constraint function are privately revealed to each agent. The loss and constraint functions are convex and can vary arbitrarily across rounds. The agents collaborate to minimize static network regret and network cumulative constraint violation. A novel distributed online algorithm with a vanishing stepsize is proposed and it achieves an O(Tmax {c,1-c}) static network regret bound and an O(T1-c/2) network cumulative constraint violation bound, where T is the number of rounds and c∈ (0,1) is a user-defined trade-off parameter. When Slater's condition holds (i.e, there is a point that strictly satisfies the inequality constraints), the network cumulative constraint violation bound is reduced to O(T1-c). Moreover, if the loss functions are strongly convex, then static network regret bound is reduced to O(log (T)), and the network cumulative constraint violation bound is reduced to O(√log (T)T) and O(log (T)) without and with Slater's condition, respectively. To the best of our knowledge, this paper is the first to achieve tighter (network) cumulative constraint violation bounds for (distributed) online convex optimization with time-varying constraints under Slater's condition. Finally, the theoretical results are verified through numerical simulations. © 1963-2012 IEEE.

关键词： Convex optimization

Long and Short-Term Constraints Driven Safe Reinforcement Learning for Autonomous Driving

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arXiv 2024年

作者： Hu, Xuemin Chen, Pan Wen, Yijun Tang, Bo Chen, Long School of Artificial Intelligence Hubei University Wuhan430062 China Key Laboratory of Intelligent Sensing System and Security Hubei University Ministry of Education Hubei Wuhan430062 China Department of Electrical and Computer Engineering Worcester Polytechnic Institute WorcesterMA01609 United States State Key Laboratory of Multimodal Artificial Intelligence Systems State Key Laboratory of Management and Control for Complex Systems Chinese Academy of Sciences Beijing100190 China WAYTOUS Inc. Beijing100083 China Shenzhen518107 China Institute of Artificial Intelligence and Robotics Xi'an Jiaotong University Xi’an710049 China

Reinforcement learning (RL) has been widely used in decision-making and control tasks, but the risk is very high for the agent in the training process due to the requirements of interaction with the environment, which seriously limits its industrial applications such as autonomous driving systems. Safe RL methods are developed to handle this issue by constraining the expected safety violation costs as a training objective, but the occurring probability of an unsafe state is still high, which is unacceptable in autonomous driving tasks. Moreover, these methods are difficult to achieve a balance between the cost and return expectations, which leads to learning performance degradation for the algorithms. In this paper, we propose a novel algorithm based on the long and short-term constraints (LSTC) for safe RL. The short-term constraint aims to enhance the shortterm state safety that the vehicle explores, while the long-term constraint enhances the overall safety of the vehicle throughout the decision-making process, both of which are jointly used to enhance the vehicle safety in the training process. In addition, we develop a safe RL method with dual-constraint optimization based on the Lagrange multiplier to optimize the training process for end-to-end autonomous driving. Comprehensive experiments were conducted on the MetaDrive simulator. Experimental results demonstrate that the proposed method achieves higher safety in continuous state and action tasks, and exhibits higher exploration performance in long-distance decision-making tasks compared with state-of-the-art methods. Copyright © 2024, The Authors. All rights reserved.

关键词： Lagrange multipliers

Quantized Distributed Nonconvex Optimization with Linear Convergence

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Quantized Distributed Nonconvex Optimization with Linear Con...

IEEE Conference on Decision and control

作者： Lei Xu Xinlei Yi Jiayue Sun Yang Shi Karl Henrik Johansson Tao Yang State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang China Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Digital Futures Stockholm Sweden Department of Mechanical Engineering University of Victoria Victoria Canada

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

This paper considers distributed nonconvex op-timization for minimizing the average of local cost functions, by using local information exchange over undirected communication networks. Since the communication channels often have limited bandwidth or capacity, we first introduce a quantization rule and an encoder/decoder scheme to reduce the transmission bits. By integrating them with a distributed algorithm, we then propose a distributed quantized nonconvex optimization algorithm. Assuming the global cost function satisfies the Polyak– Łojasiewicz condition, which does not require the global cost function to be convex and the global minimizer is not necessarily unique, we show that the proposed algorithm linearly converges to a global optimal point. Moreover, a low data rate is shown to be sufficient to ensure linear convergence when the algorithm parameters are properly chosen. The theoretical results are illustrated by numerical simulation examples.

关键词： Quantization (signal) Communication channels Bandwidth Cost function Numerical simulation Communication networks Distributed algorithms

Feedback Design for Devising Optimal Epidemic control Policies

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arXiv 2022年

作者： Niazi, Muhammad Umar B. Paré, Philip E. Johansson, Karl H. Laboratory for Information and Decision Systems Massachusetts Institute of Technology 77 Massachusetts Avenue CambridgeMA02139 United States Division of Decision and Control Systems Digital Futures School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden Elmore Family School of Electrical and Computer Engineering Purdue University IN United States

This paper proposes a feedback design that effectively copes with uncertainties for reliable epidemic monitoring and control. There are several optimization-based methods to estimate the parameters of an epidemic model by utilizing past reported data. However, due to the possibility of noise in the data, the estimated parameters may not be accurate, thereby exacerbating the model uncertainty. To address this issue, we provide an observer design that enables robust state estimation of epidemic processes, even in the presence of uncertain models and noisy measurements. Using the estimated model and state, we then devise optimal control policies by minimizing a predicted cost functional. To demonstrate the effectiveness of our approach, we implement it on a modified SIR epidemic model. The results show that our proposed method is efficient in mitigating the uncertainties that may arise in epidemic monitoring and control. © 2022, CC BY.

关键词： Robust control

Robust Data-Driven Predictive control of Unknown Nonlinear Systems using Reachability Analysis

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arXiv 2022年

作者： Farjadnia, Mahsa Alanwar, Amr Niazi, Muhammad Umar B. Molinari, Marco Johansson, Karl Henrik Department of Energy Technology School of Industrial Engineering and Management KTH Royal Institute of Technology Stockholm Sweden School of Computer Science and Engineering Constructor University Bremen Germany Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden Laboratory for Information and Decision Systems Massachusetts Institute of Technology Cambridge United States

This work proposes a robust data-driven predictive control approach for unknown nonlinear systems in the presence of bounded process and measurement noise. Data-driven reachable sets are employed for the controller design instead of using an explicit nonlinear system model. Although the process and measurement noise are bounded, the statistical properties of the noise are not required to be known. By using the past noisy input-output data in the learning phase, we propose a novel method to over-approximate exact reachable sets of an unknown nonlinear system. Then, we propose a data-driven predictive control approach to compute safe and robust control policies from noisy online data. The constraints are guaranteed in the control phase with robust safety margins by effectively using the predicted output reachable set obtained in the learning phase. Finally, a numerical example validates the efficacy of the proposed approach and demonstrates comparable performance with a model-based predictive control approach. Copyright © 2022, The Authors. All rights reserved.

关键词： Nonlinear systems

Distributed Constrained Online Nonconvex Optimization with Compressed Communication

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arXiv 2025年

作者： Zhang, Kunpeng Xu, Lei Yi, Xinlei Cao, Ming Johansson, Karl H. Chai, Tianyou Yang, Tao State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang110819 China Department of Mechanical Engineering University of Victoria VictoriaBCV8W 2Y2 Canada Shanghai Institute of Intelligent Science and Technology National Key Laboratory of Autonomous Intelligent Unmanned Systems Frontiers Science Center for Intelligent Autonomous Systems Ministry of Education Shanghai201210 China Engineering and Technology Institute Groningen Faculty of Science and Engineering University of Groningen GroningenAG 9747 Netherlands Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Sweden Digital Futures Stockholm10044 Sweden

This paper considers distributed online nonconvex optimization with time-varying inequality constraints over a network of agents. For a time-varying graph, we propose a distributed online primal–dual algorithm with compressed communication to efficiently utilize communication resources. We show that the proposed algorithm establishes an O(T max{1−θ1,θ1}) network regret bound and an O(T 1−θ1/2) network cumulative constraint violation bound, where T is the number of iterations and θ1 ∈ (0, 1) is a user-defined trade-off parameter. When Slater’s condition holds (i.e, there is a point that strictly satisfies the inequality constraints at all iterations), the network cumulative constraint violation bound is reduced to O(T 1−θ1). These bounds are comparable to the state-of-the-art results established by existing distributed online algorithms with perfect communication for distributed online convex optimization with (time-varying) inequality constraints. Finally, a simulation example is presented to validate the theoretical results. Copyright © 2025, The Authors. All rights reserved.

关键词： Convex optimization

Non-convex potential games for finding global solutions to sensor network localization

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arXiv 2023年

作者： Xu, Gehui Chen, Guanpu Hong, Yiguang Fidan, Baris Parisini, Thomas Johansson, Karl H. Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Beijing China Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm100 44 Sweden Department of Control Science and Engineering Tongji University Shanghai201804 China Shanghai Research Institute for Intelligent Autonomous Systems Shanghai201210 China Department of Mechanical and Mechatronics Engineering University of Waterloo WaterlooONN2L 3G1 Canada Department of Electrical and Electronic Engineering Imperial College London LondonSW7 2AZ United Kingdom Department of Engineering and Architecture University of Trieste Trieste34127 Italy

Sensor network localization (SNL) problems require determining the physical coordinates of all sensors in a network. This process relies on the global coordinates of anchors and the available measurements between non-anchor and anchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally optimal solution to SNL is challenging, as well as implementing corresponding algorithms. In this paper, we formulate a non-convex multi-player potential game for a generic SNL problem to investigate the identification condition of the global Nash equilibrium (NE) therein, where the global NE represents the global solution of SNL. We employ canonical duality theory to transform the non-convex game into a complementary dual problem. Then we develop a conjugation-based algorithm to compute the stationary points of the complementary dual problem. On this basis, we show an identification condition of the global NE: the stationary point of the proposed algorithm satisfies a duality relation. Finally, simulation results are provided to validate the effectiveness of the theoretical results. Copyright © 2023, The Authors. All rights reserved.

关键词： Sensor networks

Overcoming the Fear of the Dark: Occlusion-Aware Model-Predictive Planning for Automated Vehicles Using Risk Fields

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arXiv 2023年

作者： van der Ploeg, Chris Nyberg, Truls Sánchez, José Manuel Gaspar Silvas, Emilia van de Wouw, Nathan Netherlands Organisation for Applied Scientific Research Integrated Vehicle Safety Group Helmond5700 AT Netherlands Eindhoven University of Technology Dynamics and Control Group Mechanical Engineering Dept. P.O. Box 513 Eindhoven5600 MB Netherlands Eindhoven University of Technology Control Systems Technology Group Mechanical Engineering Dept. P.O. Box 513 Eindhoven5600 MB Netherlands KTH Royal Institute of Technology Division of Robotics Perception and Learning School of Electrical Engineering and Computer Science Stockholm100 44 Sweden Scania CV AB Södertälje151 87 Sweden

As vehicle automation advances, motion planning algorithms face escalating challenges in achieving safe and efficient navigation. Existing Advanced Driver Assistance Systems (ADAS) primarily focus on basic tasks, leaving unexpected scenarios for human intervention, which can be error-prone. Motion planning approaches for higher levels of automation in the state-of-the-art are primarily oriented toward the use of risk- or anti-collision constraints, using over-approximates of the shapes and sizes of other road users to prevent collisions. These methods however suffer from conservative behavior and the risk of infeasibility in high-risk initial conditions. In contrast, our work introduces a novel multi-objective trajectory generation approach. We propose an innovative method for constructing risk fields that accommodates diverse entity shapes and sizes, which allows us to also account for the presence of potentially occluded objects. This methodology is integrated into an occlusion-aware trajectory generator, enabling dynamic and safe maneuvering through intricate environments while anticipating (potentially hidden) road users and traveling along the infrastructure toward a specific goal. Through theoretical underpinnings and simulations, we validate the effectiveness of our approach. This paper bridges crucial gaps in motion planning for automated vehicles, offering a pathway toward safer and more adaptable autonomous navigation in complex urban contexts. Copyright © 2023, The Authors. All rights reserved.

关键词： Motion planning

A Communication-Efficient Decentralized Newton's Method with Provably Faster Convergence

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arXiv 2022年

作者： Liu, Huikang Zhang, Jiaojiao So, Anthony Man-Cho Ling, Qing The Research Institute for Interdisciplinary Sciences School of Information Management and Engineering Shanghai University of Finance and Economics China The Division of Decision and Control Systems School of Electrical Engineering and Computer Science Kth Royal Institute of Technology Sweden The Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong Hong Kong The School of Computer Science and Engineering Guangdong Province Key Laboratory of Computational Science Sun Yat-Sen University China The Pazhou Lab China

In this paper, we consider a strongly convex finite-sum minimization problem over a decentralized network and propose a communication-efficient decentralized Newton's method for solving it. The main challenges in designing such an algorithm come from three aspects: (i) mismatch between local gradients/ Hessians and the global ones;(ii) cost of sharing second-order information;(iii) tradeoff among computation and communication. To handle these challenges, we first apply dynamic average consensus (DAC) so that each node is able to use a local gradient approximation and a local Hessian approximation to track the global gradient and Hessian, respectively. Second, since exchanging Hessian approximations is far from communication-efficient, we require the nodes to exchange the compressed ones instead and then apply an error compensation mechanism to correct for the compression noise. Third, we introduce multistep consensus for exchanging local variables and local gradient approximations to balance between computation and communication. With novel analysis, we establish the globally linear (resp., asymptotically super-linear) convergence rate of the proposed method when m is constant (resp., tends to infinity), where m ≥ 1 is the number of consensus inner steps. To the best of our knowledge, this is the first super-linear convergence result for a communication-efficient decentralized Newton's method. Moreover, the rate we establish is provably faster than those of first-order methods. Our numerical results on various applications corroborate the theoretical findings. Copyright © 2022, The Authors. All rights reserved.

关键词： Newton-Raphson method