System‐Level Protection of Preconditioned PI Consensus Algorithms Against Eavesdropping Adversaries via Innovation‐Shared Inter‐Agent Communication

ABSTRACT Preconditioned proportional‐integral consensus ( PrecPIC ) is an efficient algorithm for solving distributed optimization problems. This work investigates its robustness against eavesdropping adversaries, whose interception capabilities are modeled by a Bernoulli process with a positive success probability and whose objective is to infer the final consensus point of distributed agents implementing the algorithm. We demonstrate that the conventional PrecPIC lacks resilience, and in fact remains vulnerable even under minimal adversarial interception probability. To address this, we propose a modified inter‐agent communication protocol that enhances protection without compromising solution accuracy or convergence rate. We analyze how the degree of protection relates to algorithm parameters, the optimization objective, and adversarial capabilities, providing a basis for principled parameter tuning. The inherent trade‐off between protection and convergence speed is also characterized. Numerical experiments validate our theoretical results and demonstrate the improved performance of the proposed modifications relative to similar enhancements applied to alternative algorithms.