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Register a new userDisturbance-resilient Distributed Resource Allocation over Stochastic Networks using Uncoordinated Stepsizes
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This paper studies distributed resource allocation problem in multi-agent systems, where all the agents cooperatively minimize the sum of their cost functions with global resource constraints over stochastic communication networks. This problem arises from many practical domains such as economic dispatch in smart grid, task assignment, and power allocation in robotic control. Most of existing works cannot converge to the optimal solution if states deviate from feasible region due to disturbance caused by environmental noise, misoperation, malicious attack, etc. To solve this problem, we propose a distributed deviation-tracking resource allocation algorithm and prove that it linearly converges to the optimal solution with constant stepsizes. We further explore its resilience properties of the proposed algorithm. Most importantly, the algorithm still converges to the optimal solution under the disturbance injection and random communication failure. In order to improve the convergence rate, the optimal stepsizes for the fastest convergence rate are established. We also prove the algorithm converges linearly to the optimal solution in mean square even with uncoordinated stepsizes, i.e., agents are allowed to employ different stepsizes. Simulations are provided to verify the theoretical results.
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We consider a resource allocation problem involving a large number of agents with individual constraints subject to privacy, and a central operator whose objective is to optimize a global, possibly nonconvex, cost while satisfying the agents constraints, for instance an energy operator in charge of the management of energy consumption flexibilities of many individual consumers. We provide a privacy-preserving algorithm that does compute the optimal allocation of resources, avoiding each agent to reveal her private information (constraints and individual solution profile) neither to the central operator nor to a third party. Our method relies on an aggregation procedure: we compute iteratively a global allocation of resources, and gradually ensure existence of a disaggregation, that is individual profiles satisfying agents private constraints, by a protocol involving the generation of polyhedral cuts and secure multiparty computations (SMC). To obtain these cuts, we use an alternate projection method, which is implemented locally by each agent, preserving her privacy needs. We adress especially the case in which the local and global constraints define a transportation polytope. Then, we provide theoretical convergence estimates together with numerical results, showing that the algorithm can be effectively used to solve the allocation problem in high dimension, while addressing privacy issues.
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Distributed processing over networks relies on in-network processing and cooperation among neighboring agents. Cooperation is beneficial when agents share a common objective. However, in many applications agents may belong to different clusters that pursue different objectives. Then, indiscriminate cooperation will lead to undesired results. In this work, we propose an adaptive clustering and learning scheme that allows agents to learn which neighbors they should cooperate with and which other neighbors they should ignore. In doing so, the resulting algorithm enables the agents to identify their clusters and to attain improved learning and estimation accuracy over networks. We carry out a detailed mean-square analysis and assess the error probabilities of Types I and II, i.e., false alarm and mis-detection, for the clustering mechanism. Among other results, we establish that these probabilities decay exponentially with the step-sizes so that the probability of correct clustering can be made arbitrarily close to one.
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