Cybersecurity in Distributed and Fully-Decentralized Optimization: Distortions, Noise Injection, and ADMM

Abstract

As problems in machine learning, smartgrid dispatch, and IoT coordination problems have grown, distributed and fully-decentralized optimization models have gained attention for providing computational scalability to optimization tools. However, in applications where consumer devices are trusted to serve as distributed computing nodes, compromised devices can expose the optimization algorithm to cybersecurity threats which have not been examined in previous literature. This paper examines potential attack vectors for generalized distributed optimization problems, with a focus on the Alternating Direction Method of Multipliers (ADMM), a popular tool for convex optimization. Methods for detecting and mitigating attacks in ADMM problems are described, and simulations demonstrate the efficacy of the proposed models. The weaknesses of fully-decentralized optimization schemes, in which nodes communicate directly with neighbors, is demonstrated, and a number of potential architectures for providing security to these networks is discussed.

Analyzing Malicious Data Injection Attacks on Distributed Optimal Power Flow Algorithms

“…The detection models discussed above are data-driven with no detectability guarantees. Conversely, [10] proposes an analytical detection method for convex problems via checking the convexity of the attacker's subproblem in the ADMM algorithm. The method in [10] estimates the Hessian matrices for the objectives of the neighboring agents' local subproblems.…”

“…Conversely, [10] proposes an analytical detection method for convex problems via checking the convexity of the attacker's subproblem in the ADMM algorithm. The method in [10] estimates the Hessian matrices for the objectives of the neighboring agents' local subproblems. If the estimated Hessians are not positive semidefinite, which is necessary for convexity, then there is data manipulation.…”

“…Moreover, numerical issues may arise due to poor matrix conditioning when estimating the Hessian matrices, especially for subproblem solutions that are close to the optimal solution. Thus, [10] uses additional shared data iterates to improve conditioning at the expense of more computations. Nevertheless, these challenges may cause inaccurate estimations, potentially resulting in false negatives.…”

“…Nevertheless, these challenges may cause inaccurate estimations, potentially resulting in false negatives. Moreover, the method in [10] is only applicable to convex problems. This paper investigates the vulnerability of the ADMM algorithm to elaborate data manipulation attacks.…”

Revealing a New Vulnerability of Distributed State Estimation: A Data Integrity Attack and an Unsupervised Detection Algorithm

“…A comparison between the performance of the centralized and decentralized detectors is made in [20] and it is shown that each detector can outperform the other ones on a certain system and attack configurations. Recently blockchain-based systems on peer-to-peer networks are proposed for securing the distributed applications of power systems (e.g., the DSE) [21], [22].…”