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We study a distributed method called SAB–TV, which employs gradient tracking to collaboratively minimize the strongly-convex sum of smooth local cost functions for networked agents communicating over a time-varying directed graph. Each agent, assumed to have access to a stochastic first order oracle for obtaining an unbiased estimate of the gradient of its local cost function, maintains an auxiliary variable to asymptotically track the stochastic gradient of the global cost. The optimal decision and gradient tracking are updated over time through limited information exchange with local neighbors using row- and column-stochastic weights, guaranteeing both consensus and optimality. With a sufficiently small constant step-size, we demonstrate that, in expectation, SAB–TV converges linearly to a neighborhood of the optimal solution. Numerical simulations illustrate the effectiveness of the proposed algorithm.more » « less
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Matni, N.; Morari, M.; Pappas, G. J. (Ed.)We address the problem of learning the legitimacy of other agents in a multiagent network when an unknown subset is comprised of malicious actors. We specifically derive results for the case of directed graphs and where stochastic side information, or observations of trust, is available. We refer to this as “learning trust” since agents must identify which neighbors in the network are reliable, and we derive a learning protocol to achieve this. We also provide analytical results showing that under this protocol i) agents can learn the legitimacy of all other agents almost surely, and ii) the opinions of the agents converge in mean to the true legitimacy of all other agents in the network. Lastly, we provide numerical studies showing that our convergence results hold for various network topologies and variations in the number of malicious agents.more » « less
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