Many distributed systems require consensus that is accurate, private, and resilient to adversaries, yet per-round payloads are fixed, making convergence speed the dominant communications/energy cost. We introduce a two-stage offline weight-design method that (i) respects a local state-augmentation scheme ensuring structural non-observability of each agent's initial value, and (ii) optimizes weights on all exclusion-set subnetworks that support resilience to up to f adversarial agents under a first-deviation rule. We prove that the optimized weights preserve consensus correctness and the privacy/resilience structure, and we minimize a spectral proxy (the second-largest eigenvalue modulus) for the convergence rate under row-stochastic and sparsity constraints. On Erdős–Rényi and Watts–Strogatz digraphs with injected adversaries, the method reduces iterations to ϵ-accuracy by 30–42% (median across 50 trials per setting), with unchanged per-round communication; thus total neighbor transmissions fall proportionally. We report offline compute costs, sensitivity to detection thresholds, and release code to reproduce all results.
Moniz et al. (Thu,) studied this question.