97,958 research outputs found

    Gradient-tracking Based Differentially Private Distributed Optimization with Enhanced Optimization Accuracy

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    Privacy protection has become an increasingly pressing requirement in distributed optimization. However, equipping distributed optimization with differential privacy, the state-of-the-art privacy protection mechanism, will unavoidably compromise optimization accuracy. In this paper, we propose an algorithm to achieve rigorous ϵ\epsilon-differential privacy in gradient-tracking based distributed optimization with enhanced optimization accuracy. More specifically, to suppress the influence of differential-privacy noise, we propose a new robust gradient-tracking based distributed optimization algorithm that allows both stepsize and the variance of injected noise to vary with time. Then, we establish a new analyzing approach that can characterize the convergence of the gradient-tracking based algorithm under both constant and time-varying stespsizes. To our knowledge, this is the first analyzing framework that can treat gradient-tracking based distributed optimization under both constant and time-varying stepsizes in a unified manner. More importantly, the new analyzing approach gives a much less conservative analytical bound on the stepsize compared with existing proof techniques for gradient-tracking based distributed optimization. We also theoretically characterize the influence of differential-privacy design on the accuracy of distributed optimization, which reveals that inter-agent interaction has a significant impact on the final optimization accuracy. The discovery prompts us to optimize inter-agent coupling weights to minimize the optimization error induced by the differential-privacy design. Numerical simulation results confirm the theoretical predictions

    A Differential Private Method for Distributed Optimization in Directed Networks via State Decomposition

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    In this paper, we study the problem of consensus-based distributed optimization where a network of agents, abstracted as a directed graph, aims to minimize the sum of all agents' cost functions collaboratively. In existing distributed optimization approaches (Push-Pull/AB) for directed graphs, all agents exchange their states with neighbors to achieve the optimal solution with a constant stepsize, which may lead to the disclosure of sensitive and private information. For privacy preservation, we propose a novel state-decomposition based gradient tracking approach (SD-Push-Pull) for distributed optimzation over directed networks that preserves differential privacy, which is a strong notion that protects agents' privacy against an adversary with arbitrary auxiliary information. The main idea of the proposed approach is to decompose the gradient state of each agent into two sub-states. Only one substate is exchanged by the agent with its neighbours over time, and the other one is kept private. That is to say, only one substate is visible to an adversary, protecting the privacy from being leaked. It is proved that under certain decomposition principles, a bound for the sub-optimality of the proposed algorithm can be derived and the differential privacy is achieved simultaneously. Moreover, the trade-off between differential privacy and the optimization accuracy is also characterized. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed approach

    A Distributed Optimization Method for Optimal Energy Management in Smart Grid

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    This chapter presents a distributed optimization method named sequential distributed consensus-based ADMM for solving nonlinear constrained convex optimization problems arising in smart grids in order to derive optimal energy management strategies. To develop such distributed optimization method, multi-agent system and consensus theory are employed. Next, two smart grid problems are investigated and solved by the proposed distributed algorithm. The first problem is called the dynamic social welfare maximization problem where the objective is to simultaneously minimize the generation costs of conventional power plants and maximize the satisfaction of consumers. In this case, there are renewable energy sources connected to the grid, but energy storage systems are not considered. On the other hand, in the second problem, plug-in electric vehicles are served as energy storage systems, and their charging or discharging profiles are optimized to minimize the overall system operation cost. It is then shown that the proposed distributed optimization algorithm gives an efficient way of energy management for both problems above. Simulation results are provided to illustrate the proposed theoretical approach

    Differential Games For Multi-agent Systems Under Distributed Information

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    In this dissertation, we consider differential games for multi-agent systems under distributed information where every agent is only able to acquire information about the others according to a directed information graph of local communication/sensor networks. Such games arise naturally from many applications including mobile robot coordination, power system optimization, multiplayer pursuit-evasion games, etc. Since the admissible strategy of each agent has to conform to the information graph constraint, the conventional game strategy design approaches based upon Riccati equation(s) are not applicable because all the agents are required to have the information of the entire system. Accordingly, the game strategy design under distributed information is commonly known to be challenging. Toward this end, we propose novel open-loop and feedback game strategy design approaches for Nash equilibrium and noninferior solutions with a focus on linear quadratic differential games. For the open-loop design, approximate Nash/noninferior game strategies are proposed by integrating distributed state estimation into the open-loop global-information Nash/noninferior strategies such that, without global information, the distributed game strategies can be made arbitrarily close to and asymptotically converge over time to the global-information strategies. For the feedback design, we propose the best achievable performance indices based approach under which the distributed strategies form a Nash equilibrium or noninferior solution with respect to a set of performance indices that are the closest to the original indices. This approach overcomes two issues in the classical optimal output feedback approach: the simultaneous optimization and initial state dependence. The proposed open-loop and feedback design approaches are applied to an unmanned aerial vehicle formation control problem and a multi-pursuer single-evader differential game problem, respectively. Simulation results of several scenarios are presented for illustration

    Multi-Agent Reinforcement Learning-Based Buffer-Aided Relay Selection in IRS-Assisted Secure Cooperative Networks

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    This paper proposes a multi-agent deep reinforcement learning-based buffer-aided relay selection scheme for an intelligent reflecting surface (IRS)-assisted secure cooperative network in the presence of an eavesdropper. We consider a practical phase model where both phase shift and reflection amplitude are discrete variables to vary the reflection coefficients of the IRS. Furthermore, we introduce the buffer-aided relay to enhance the secrecy performance, but the use of the buffer leads to the cost of delay. Thus, we aim to maximize either the average secrecy rate with a delay constraint or the throughput with both delay and secrecy constraints, by jointly optimizing the buffer-aided relay selection and the IRS reflection coefficients. To obtain the solution of these two optimization problems, we divide each of the problems into two sub-tasks and then develop a distributed multi-agent reinforcement learning scheme for the two cooperative sub-tasks, each relay node represents an agent in the distributed learning. We apply the distributed reinforcement learning scheme to optimize the IRS reflection coefficients, and then utilize an agent on the source to learn the optimal relay selection based on the optimal IRS reflection coefficients in each iteration. Simulation results show that the proposed learning-based scheme uses an iterative approach to learn from the environment for approximating an optimal solution via the exploration of multiple agents, which outperforms the benchmark schemes

    Decentralized Coalition Formation with Agent-based Combinatorial Heuristics

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    A steadily growing pervasion of the energy distribution grid with communication technology is widely seen as an enabler for new computational coordination techniques for renewable, distributed generation as well as for bundling with controllable consumers. Smart markets will foster a decentralized grid management. One important task as prerequisite to decentralized management is the ability to group together in order to jointly gain enough suitable flexibility and capacity to assume responsibility for a specific control task in the grid. In self-organized smart grid scenarios, grouping or coalition formation has to be achieved in a decentralized and situation aware way based on individual capabilities. We present a fully decentralized coalition formation approach based on an established agent-based heuristics for predictive scheduling with the additional advantage of keeping all information about local decision base and local operational constraints private. Two closely interlocked optimization processes orchestrate an overall procedure that adapts a coalition structure to best suit a given set of energy products. The approach is evaluated in several simulation scenarios with different type of established models for integrating distributed energy resources and is also extended to the induced use case of surplus distribution using basically the same algorithm

    An Algorithm for Multi-Objective Multi-Agent Optimization

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    Multi-agent optimization problems with many objective functions have drawn much interest over the past two decades. Many works on the subject minimize the sum of objective functions, which implicitly carries a decision about the problem formulation. Indeed, it represents a special case of a multi-objective problem, in which all objectives are prioritized equally. To the best of our knowledge, multi-objective optimization applied to multi-agent systems remains largely unexplored. Therefore, we propose a distributed algorithm that allows the exploration of Pareto optimal solutions for the non-homogeneously weighted sum of objective functions. In the problems we consider, each agent has one objective function to minimize based on a gradient method. Agents update their decision variables by exchanging information with other agents in the network. Information exchanges are weighted by each agent's individual weights that encode the extent to which they prioritize other agents' objectives. This paper provides a proof of convergence, performance bounds, and explicit limits for the results of agents' computations. Simulation results with different sizes of networks demonstrate the efficiency of the proposed approach and how the choice of weights impacts the agents' final result
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