This paper considers the problem of privacy preservation against passive internal and external malicious agents in the continuous-time Laplacian average consensus algorithm over strongly connected and weight-balanced digraphs. For this problem, we evaluate the effectiveness of use of additive perturbation signals as a privacy preservation measure against malicious agents that know the graph topology. Our results include (a) identifying the necessary and sufficient conditions on admissible additive perturbation signals that do not perturb the convergence point of the algorithm from the average of initial values of the agents; (b) obtaining the necessary and sufficient condition on the knowledge set of a malicious agent that enables it to identify the initial value of another agent; (c) designing observers that internal and external malicious agents can use to identify the initial conditions of another agent when their knowledge set on that agent enables them to do so. We demonstrate our results through a numerical example.

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This paper considers a multi-agent submodular set function maximization problem subject to partition matroid in which the utility is shared, but the agents' policy choices are constrained locally. The paper's main contribution is a distributed algorithm that enables each agent to find a suboptimal policy locally with a guaranteed level of privacy. The submodular set function maximization problems are NP-hard. For agents communicating over a connected graph, this paper proposes a polynomial-time distributed algorithm to obtain a guaranteed near optimal solution. The proposed algorithm is based on a distributed randomized gradient ascent scheme on the multilinear extension of the submodular set function in the continuous domain. Our next contribution is the design of a distributed rounding algorithm that does not need any inter-agent communication. We base our algorithm's privacy preservation characteristic on our proposed stochastic rounding method and tie the level of privacy to the variable γ ∈ [0, 1]. That is, the policy choice of an agent can be determined with the probability of at most γ. We show that our distributed algorithm results in a strategy set that when the team's objective function is evaluated in the worst case, the objective function value is in 1 − (1/e) h(γ) − O(1/T ) of the optimal solution, highlighting the interplay between level of optimality gap and guaranteed level of privacy where T is the number of communication rounds between the agents.

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