Biblio

This paper studies the security issue of a gossip-based distributed projected gradient (DPG) algorithm, when it is applied for solving a decentralized multi-agent optimization. It is known that the gossip-based DPG algorithm is vulnerable to insider attacks because each agent locally estimates its (sub)gradient without any supervision. This work leverages the convolutional neural network (CNN) to perform the detection and localization of the insider attackers. Compared to the previous work, CNN can learn appropriate decision functions from the original state information without preprocessing through artificially designed rules, thereby alleviating the dependence on complex pre-designed models. Simulation results demonstrate that the proposed CNN-based approach can effectively improve the performance of detecting and localizing malicious agents, as compared with the conventional pre-designed score-based model.

Distributed optimization algorithms are proposed to, potentially, reduce the computational time of large-scale optimization problems, such as security-constrained economic dispatch (SCED). While various geographical decomposition strategies have been presented in the literature, we proposed a temporal decomposition strategy to divide the SCED problem over the considered scheduling horizon. The proposed algorithm breaks SCED over the scheduling time and takes advantage of parallel computing using multi-core machines. In this paper, we investigate how to partition the overall time horizon. We study the effect of the number of partitions (i.e., SCED subproblems) on the overall performance of the distributed coordination algorithm and the effect of partitioning time interval on the optimal solution. In addition, the impact of system loading condition and ramp limits of the generating units on the number of iterations and solution time are analyzed. The results show that by increasing the number of subproblems, the computational burden of each subproblem is reduced, but more shared variables and constraints need to be modeled between the subproblems. This can result in increasing the total number of iterations and consequently the solution time. Moreover, since the load behavior affects the active ramping between the subproblems, the breaking hour determines the difference between shared variables. Hence, the optimal number of subproblems is problem dependent. A 3-bus and the IEEE 118-bus system are selected to analyze the effect of the number of partitions.

This paper discusses formulations and algorithms which allow a number of agents to collectively solve problems involving both (non-convex) minimization and (concave) maximization operations. These problems have a number of interesting applications in information processing and machine learning, and in particular can be used to model an adversary learning problem called network data poisoning. We develop a number of algorithms to efficiently solve these non-convex min-max optimization problems, by combining techniques such as gradient tracking in the decentralized optimization literature and gradient descent-ascent schemes in the min-max optimization literature. Also, we establish convergence to a first order stationary point under certain conditions. Finally, we perform experiments to demonstrate that the proposed algorithms are effective in the data poisoning attack.

Distributed consensus is a prototypical distributed optimization and decision making problem in social, economic and engineering networked systems. In collaborative applications investigating the effects of adversaries is a critical problem. In this paper we investigate distributed consensus problems in the presence of adversaries. We combine key ideas from distributed consensus in computer science on one hand and in control systems on the other. The main idea is to detect Byzantine adversaries in a network of collaborating agents who have as goal reaching consensus, and exclude them from the consensus process and dynamics. We describe a novel trust-aware consensus algorithm that integrates the trust evaluation mechanism into the distributed consensus algorithm and propose various local decision rules based on local evidence. To further enhance the robustness of trust evaluation itself, we also introduce a trust propagation scheme in order to take into account evidences of other nodes in the network. The resulting algorithm is flexible and extensible, and can incorporate more complex designs of decision rules and trust models. To demonstrate the power of our trust-aware algorithm, we provide new theoretical security performance results in terms of miss detection and false alarm rates for regular and general trust graphs. We demonstrate through simulations that the new trust-aware consensus algorithm can effectively detect Byzantine adversaries and can exclude them from consensus iterations even in sparse networks with connectivity less than 2f+1, where f is the number of adversaries.

Nowadays, many applications involve big data and big data analysis methods appear in many fields. As a preliminary attempt to solve the challenge of big data analysis, this paper presents a distributed online learning algorithm based on differential privacy. Since online learning can effectively process sensitive data, we introduce the concept of differential privacy in distributed online learning algorithms, with the aim at ensuring data privacy during online learning to prevent adversarial nodes from inferring any important data information. In particular, for different adversary models, we consider different type graphs to tolerate a limited number of adversaries near each regular node or tolerate a global limited number of adversaries.

This paper addresses the problem of distributed multi-agent optimization in which each agent i has a local cost function hi(x), and the goal is to optimize a global cost function that aggregates the local cost functions. Such optimization problems are of interest in many contexts, including distributed machine learning, distributed resource allocation, and distributed robotics. We consider the distributed optimization problem in the presence of faulty agents. We focus primarily on Byzantine failures, but also briey discuss some results for crash failures. For the Byzantine fault-tolerant optimization problem, the ideal goal is to optimize the average of local cost functions of the non-faulty agents. However, this goal also cannot be achieved. Therefore, we consider a relaxed version of the fault-tolerant optimization problem. The goal for the relaxed problem is to generate an output that is an optimum of a global cost function formed as a convex combination of local cost functions of the non-faulty agents. More precisely, there must exist weights αi for i∈N such that αi ≥ 0 and ∑i≥ Nαi=1, and the output is an optimum of the cost function ∑i≥ N αihi(x). Ideally, we would like αi=1/textbarNtextbar for all i≥ N, however, this cannot be guaranteed due to the presence of faulty agents. In fact, the maximum number of nonzero weights (αi's) that can be guaranteed is textbarNtextbar-f, where f is the maximum number of Byzantine faulty agents. We present an iterative distributed algorithm that achieves optimal fault-tolerance. Specifically, it ensures that at least textbarNtextbar-f agents have weights that are bounded away from 0 (in particular, lower bounded by 1/2textbarNtextbar-f\vphantom\\). The proposed distributed algorithm has a simple iterative structure, with each agent maintaining only a small amount of local state. We show that the iterative algorithm ensures two properties as time goes to ∞: consensus (i.e., output of non-faulty agents becomes identical in the time limit), and optimality (in the sense that the output is the optimum of a suitably defined global cost function).

Game theory serves as a powerful tool for distributed optimization in multiagent systems in different applications. In this paper we consider multiagent systems that can be modeled as a potential game whose potential function coincides with a global objective function to be maximized. This approach renders the agents the strategic decision makers and the corresponding optimization problem the problem of learning an optimal equilibruim point in the designed game. In distinction from the existing works on the topic of payoff-based learning, we deal here with the systems where agents have neither memory nor ability for communication, and they base their decision only on the currently played action and the experienced payoff. Because of these restrictions, we use the methods of reinforcement learning, stochastic approximation, and learning automata extensively reviewed and analyzed in [3], [9]. These methods allow us to set up the agent dynamics that moves the game out of inefficient Nash equilibria and leads it close to an optimal one in both cases of discrete and continuous action sets.

Distributed optimization is an emerging research topic. Agents in the network solve the problem by exchanging information which depicts people's consideration on a optimization problem in real lives. In this paper, we introduce two algorithms in continuous-time to solve distributed optimization problems with equality constraints where the cost function is expressed as a sum of functions and where each function is associated to an agent. We firstly construct a continuous dynamic system by utilizing the Lagrangian function and then show that the algorithm is locally convergent and globally stable under certain conditions. Then, we modify the Lagrangian function and re-construct the dynamic system to prove that the new algorithm will be convergent under more relaxed conditions. At last, we present some simulations to prove our theoretical results.

In this paper, we consider distributed algorithm based on a continuous-time multi-agent system to solve constrained optimization problem. The global optimization objective function is taken as the sum of agents' individual objective functions under a group of convex inequality function constraints. Because the local objective functions cannot be explicitly known by all the agents, the problem has to be solved in a distributed manner with the cooperation between agents. Here we propose a continuous-time distributed gradient dynamics based on the KKT condition and Lagrangian multiplier methods to solve the optimization problem. We show that all the agents asymptotically converge to the same optimal solution with the help of a constructed Lyapunov function and a LaSalle invariance principle of hybrid systems.