Algorithm-Level Confidentiality for Average Consensus on Time-Varying Directed Graphs

Abstract

Average consensus plays a key role in distributed networks, with applications ranging from time synchronization, information fusion, load balancing, to decentralized control. Existing average consensus algorithms require individual agents to exchange explicit state values with their neighbors, which leads to the undesirable disclosure of sensitive information in the state. In this paper, we propose a novel average consensus algorithm for time-varying directed graphs that can protect the confidentiality of a participating agent against other participating agents. The algorithm injects randomness in interaction to obfuscate information on the algorithm-level and can ensure information-theoretic privacy without the assistance of any trusted third party or data aggregator. By leveraging the inherent robustness of consensus dynamics against random variations in interaction, our proposed algorithm can also guarantee the accuracy of average consensus. The algorithm is distinctly different from differential-privacy based average consensus approaches which enable confidentiality through compromising accuracy in obtained consensus value. Numerical simulations confirm the effectiveness and efficiency of our proposed approach.

Decentralized Gradient Methods with Time-varying Uncoordinated Stepsizes: Convergence Analysis and Privacy Design

“…Every agent j computes and sends v k ij (defined in (35)) to all agents i ∈ N j where {W 2 } ij denotes the (i, j)th entry of matrix W 2 :…”

“…Motivated by this observation and inspired by our recent finding that interaction dynamics can be judiciously manipulated to enable privacy [33], [34], [35], we propose the following decentralized gradient algorithm to enable privacy (with per-agent version given in Algorithm PDG-DS on the next page):…”

“…Furthermore, compared with PDG-DS, the PDG-NDS algorithm can provide the same defined privacy but faster convergence to the exact optimal solution due to the non-vanishing stepsize. However, PDG-NDS needs every agent to store its variables in the preceding two iterations whereas PDG-DS only needs to store variables in one preceding iteration (compare (35) with ( 5)).…”

“…Inspired by our recent results that privacy can be enabled in consensus by manipulating inherent dynamics [33], [34], [35], we propose to enable privacy in decentralized gradient methods by judiciously manipulating the inherent dynamics of information mixing and gradient operations. More specifically, leveraging a judiciously designed mixing matrix and timevarying uncoordinated stepsizes, we propose two privacypreserving decentralized gradient based algorithms, one with diminishing stepsizes and the other one with non-diminishing stepsizes.…”

Decentralized Stochastic Optimization with Inherent Privacy Protection

“…Inspired by our recent finding that the privacy of participating agents in decentralized consensus computations can be ensured by manipulating inherent consensus dynamics [46], [47], [48], in this paper, we propose to enable intrinsic privacy protection in decentralized stochastic gradient methods by judiciously manipulating the inherent dynamics of inter-agent information fusion and gradient-descent operations. More specifically, we let each participating agent use time-varying and heterogeneous stepsize and an additional stochastic mixing coefficient to obscure its gradients when sharing information with its neighbors.…”