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This paper investigates privacy issues in distributed resource allocation over directed networks, where each agent holds a private cost function and optimizes its decision subject to a global coupling constraint through local interaction with other agents. Conventional methods for resource allocation over directed networks require all agents to transmit their original data to neighbors, which poses the risk of disclosing sensitive and private information. To address this issue, we propose an algorithm called differentially private dual gradient tracking (DP-DGT) for distributed resource allocation, which obfuscates the exchanged messages using independent Laplacian noise. Our algorithm ensures that the agents' decisions converge to a neighborhood of the optimal solution almost surely. Furthermore, without the assumption of bounded gradients, we prove that the cumulative differential privacy loss under the proposed algorithm is finite even when the number of iterations goes to infinity. To the best of our knowledge, we are the first to simultaneously achieve these two goals in distributed resource allocation problems over directed networks. Finally, numerical simulations on economic dispatch problems within the IEEE 14-bus system illustrate the effectiveness of our proposed algorithm.

Over-the-air aggregation has attracted widespread attention for its potential advantages in task-oriented applications, such as distributed sensing, learning, and consensus. In this paper, we develop a communication-efficient distributed average consensus protocol by utilizing over-the-air aggregation, which exploits the superposition property of wireless channels rather than combat it. Noisy channels and non-coherent transmission are taken into account, and only half-duplex transceivers are required. We prove that the system can achieve average consensus in mean square and even almost surely under the proposed protocol. Furthermore, we extend the analysis to the scenarios with time-varying topology. Numerical simulation shows the effectiveness of the proposed protocol.

In recent years, over-the-air aggregation has been widely considered in large-scale distributed learning, optimization, and sensing. In this paper, we propose the over-the-air federated policy gradient algorithm, where all agents simultaneously broadcast an analog signal carrying local information to a common wireless channel, and a central controller uses the received aggregated waveform to update the policy parameters. We investigate the effect of noise and channel distortion on the convergence of the proposed algorithm, and establish the complexities of communication and sampling for finding an $\epsilon$-approximate stationary point. Finally, we present some simulation results to show the effectiveness of the algorithm., Comment: To appear at IEEE ICC 2024

In this paper, we study the sensor selection problem for remote state estimation under the Quality-of-Service (QoS) requirement constraints. Multiple sensors are employed to observe a linear time-invariant system, and their measurements should be transmitted to a remote estimator for state estimation. However, due to the limited communication resources and the QoS requirement constraints, only some of the sensors can be allowed to transmit their measurements. To estimate the system state as accurately as possible, it is essential to select sensors for transmission appropriately. We formulate the sensor selection problem as a non-convex optimization problem. It is difficult to solve such a problem and even to find a feasible solution. To obtain a solution which can achieve good estimation performance, we first reformulate and relax the formulated problem. Then, we propose an algorithm based on successive convex approximation (SCA) to solve the relaxed problem. By utilizing the solution of the relaxed problem, we propose a heuristic sensor selection algorithm which can provide a good suboptimal solution. Simulation results are presented to show the effectiveness of the proposed heuristic.

In this paper, we consider using simultaneous wireless information and power transfer (SWIPT) to recharge the sensor in the LQG control, which provides a new approach to prolonging the network lifetime. We analyze the stability of the proposed system model and show that there exist two critical values for the power splitting ratio {\alpha}. Then, we propose an optimization problem to derive the optimal value of {\alpha}. This problem is non-convex but its numerical solution can be derived by our proposed algorithm efficiently. Moreover, we provide the feasible condition of the proposed optimization problem. Finally, simulation results are presented to verify and illustrate the main theoretical results.

In this paper, we propose a Bi-layer Predictionbased Reduction Branch (BP-RB) framework to speed up the process of finding a high-quality feasible solution for Mixed Integer Programming (MIP) problems. A graph convolutional network (GCN) is employed to predict binary variables' values. After that, a subset of binary variables is fixed to the predicted value by a greedy method conditioned on the predicted probabilities. By exploring the logical consequences, a learning-based problem reduction method is proposed, significantly reducing the variable and constraint sizes. With the reductive sub-MIP problem, the second layer GCN framework is employed to update the prediction for the remaining binary variables' values and to determine the selection of variables which are then used for branching to generate the Branch and Bound (B&B) tree. Numerical examples show that our BP-RB framework speeds up the primal heuristic and finds the feasible solution with high quality., Comment: This paper has been accepted for the publication of ICARCV 2022

This paper investigates sensor scheduling for state estimation of complex networks over shared transmission channels. For a complex network of dynamical systems, referred to as nodes, a sensor network is adopted to measure and estimate the system states in a distributed way, where a sensor is used to measure a node. The estimates are transmitted from sensors to the associated nodes, in the presence of one-step time delay and subject to packet loss. Due to limited transmission capability, only a portion of sensors are allowed to send information at each time step. The goal of this paper is to seek an optimal sensor scheduling policy minimizing the overall estimation errors. Under a distributed state estimation framework, this problem is reformulated as a Markov decision process, where the one-stage reward for each node is strongly coupled. The feasibility of the problem reformulation is ensured. In addition, an easy-to-check condition is established to guarantee the existence of an optimal deterministic and stationary policy. Moreover, it is found that the optimal policies have a threshold, which can be used to reduce the computational complexity in obtaining these policies. Finally, the effectiveness of the theoretical results is illustrated by several simulation examples.

In this paper, we surveyed the existing literature studying different approaches and algorithms for the four critical components in the general branch and bound (B&B) algorithm, namely, branching variable selection, node selection, node pruning, and cutting-plane selection. However, the complexity of the B&B algorithm always grows exponentially with respect to the increase of the decision variable dimensions. In order to improve the speed of B&B algorithms, learning techniques have been introduced in this algorithm recently. We further surveyed how machine learning can be used to improve the four critical components in B&B algorithms. In general, a supervised learning method helps to generate a policy that mimics an expert but significantly improves the speed. An unsupervised learning method helps choose different methods based on the features. In addition, models trained with reinforcement learning can beat the expert policy, given enough training and a supervised initialization. Detailed comparisons between different algorithms have been summarized in our survey. Finally, we discussed some future research directions to accelerate and improve the algorithms further in the literature., Comment: Preprint submitted to Discrete Optimization

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.

Average consensus is extensively used in distributed networks for computation and control, where all the agents constantly communicate with each other and update their states in order to reach an agreement. Under a general average consensus algorithm, information exchanged through wireless or wired communication networks could lead to the disclosure of sensitive and private information. In this paper, we propose a privacy-preserving push-sum approach for directed networks that can protect the privacy of all agents while achieving average consensus simultaneously. Each node decomposes its initial state arbitrarily into two substates, and their average equals to the initial state, guaranteeing that the agent's state will converge to the accurate average consensus. Only one substate is exchanged by the node with its neighbours over time, and the other one is reserved. That is to say, only the exchanged substate would be visible to an adversary, preventing the initial state information from leakage. Different from the existing state-decomposition approach which only applies to undirected graphs, our proposed approach is applicable to strongly connected digraphs. In addition, in direct contrast to offset-adding based privacy-preserving push-sum algorithm, which is vulnerable to an external eavesdropper, our proposed approach can ensure privacy against both an honest-but-curious node and an external eavesdropper. A numerical simulation is provided to illustrate the effectiveness of the proposed approach.

We consider the problem of communication allocation for remote state estimation in a cognitive radio sensor network~(CRSN). A sensor collects measurements of a physical plant, and transmits the data to a remote estimator as a secondary user (SU) in the shared network. The existence of the primal users (PUs) brings exogenous uncertainties into the transmission scheduling process, and how to design an event-based scheduling scheme considering these uncertainties has not been addressed in the literature. In this work, we start from the formulation of a discrete-time remote estimation process in the CRSN, and then analyze the hidden information contained in the absence of data transmission. In order to achieve a better tradeoff between estimation performance and communication consumption, we propose both open-loop and closed-loop schedules using the hidden information under a Bayesian setting. The open-loop schedule does not rely on any feedback signal but only works for stable plants. For unstable plants, a closed-loop schedule is designed based on feedback signals. The parameter design problems in both schedules are efficiently solved by convex programming. Numerical simulations are included to illustrate the theoretical results., Comment: This paper was accepted by IEEE Transaction on Automatic Control and was published as an early access on July 7 2020

In this paper, we consider a remote state estimation problem in the presence of an eavesdropper. A smart sensor takes measurement of a discrete linear time-invariant (LTI) process and sends its local state estimate through a wireless network to a remote estimator. An eavesdropper can overhear the sensor transmissions with a certain probability. To enhance the system privacy level, we propose a novel encryption strategy to minimize a linear combination of the expected error covariance at the remote estimator and the negative of the expected error covariance at the eavesdropper, taking into account the cost of the encryption process. We prove the existence of an optimal deterministic and Markovian policy for such an encryption strategy over a finite time horizon. Two situations, namely, with or without knowledge of the eavesdropper estimation error covariance are studied and the optimal schedule is shown to satisfy the threshold-like structure in both cases. Numerical examples are given to illustrate the results., Comment: American Control Conference paper acceptance