Privacy-Preserving Average Consensus: Fundamental Analysis and a Generic Framework Design
Bibliographic record
Abstract
Average consensus is a key component of multi-agent systems coordination, while data privacy becomes a serious concern. Through the information exchange process, the initial state of an agent may be disclosed to its neighbors. The existing privacy-preserving research mainly addressed the situation of single-neighbor eavesdropping and infinite-time consensus, and they cannot deal with the cases of multi-neighbors eavesdropping and collusion inference attack or ensuring finite-time consensus. In this paper, we prove that it is impossible to preserve a node’s data privacy if all of its neighbors collusively infer the data. Otherwise, we propose a privacy-preserving framework to support conventional average consensus, push-sum consensus, and finite-time average consensus, which integrates multiplying random variables, finite-time error compensation, and updating rule jump. In this paper, each agent exchanges data with its neighbors by multiplying a random variable to its real-time state at each iteration. To eliminate errors caused by the random multiplier, a finite-time error compensation term and updating rule jump are designed, which ensure the accuracy of consensus. We prove that the proposed framework can converge and preserve privacy facing collusion inference attacks in both finite-time and infinite-time consensus, while traditional adding-noise-based methods cannot solve the finite-time case. We also derive the analytical expressions of the maximum privacy disclosure probability for the initial state of each agent, and present the impact of multiplying random variables. Extensive case studies demonstrate the effectiveness of the proposed framework.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".