On The Detection of Shared Data Manipulation In Distributed Optimization

This paper investigates the vulnerability of the Alternating Direction Method of Multipliers (ADMM) algorithm to shared data manipulation. Deliberate data manipulation may cause the ADMM algorithm to converge to suboptimal solutions. We derive a sufficient condition for detecting data manipulation based on the theoretical convergence trajectory of the ADMM algorithm. We evaluate the performance of the detection condition on three data manipulation strategies with various levels of complexity and stealth. The simplest attack sends the target values in each iteration, the second attack uses a feedback loop to find the next target values, and the last attack uses bilevel optimization to find the target values. We then extend the three data manipulation strategies to avoid detection by the proposed detection methods. We also propose an adversarial neural network training framework to detect shared data manipulation. We demonstrate the performance of our data-manipulation strategy and detection framework on optimal power flow (OPF) problems. The results show that the proposed detection condition successfully detects most of the data manipulation attacks. However, the bilevel optimization attack strategy that incorporates the detection methods may avoid detection. Countering this, our proposed adversarial training framework detects all instances of the bilevel optimization attack.