Abstract:

This talk considers the problem of resilient distributed multi-agent optimization for cyberphysical systems in the presence of malicious or non-cooperative agents. It is assumed that stochastic values of trust between agents are available which allows agents to learn their trustworthy neighbors simultaneously with performing updates to minimize their own local objective functions. The development of this trustworthy computational model combines the tools from statistical learning and distributed consensus-based optimization. Specifically, we derive a unified mathematical framework to characterize convergence, deviation of the consensus from the true consensus value, and expected convergence rate, when there exists additional information of trust between agents. Under certain conditions, we show  that the consensus protocol has almost sure convergence to a common limit value is possible even when malicious agents constitute more than half of the network;  the deviation of the converged limit, from the nominal no attack case can be bounded with probability that approaches 1 exponentially, and that correct classification of malicious and legitimate agents can be attained in (random) finite time almost surely. Further, the expected convergence rate decays exponentially with the quality of the trust observations between agents. We then combine the trust-learning model within a distributed gradient-based method for solving a multi-agent optimization problem and characterize its performance.