  The gossip-based distributed algorithms are widely used to solve
decentralized optimization problems in various multi-agent applications, while
they are generally vulnerable to data injection attacks by internal malicious
agents as each agent locally estimates its decent direction without an
authorized supervision. In this work, we explore the application of artificial
intelligence (AI) technologies to detect internal attacks. We show that a
general neural network is particularly suitable for detecting and localizing
the malicious agents, as they can effectively explore nonlinear relationship
underlying the collected data. Moreover, we propose to adopt one of the
state-of-art approaches in federated learning, i.e., a collaborative
peer-to-peer machine learning protocol, to facilitate training our neural
network models by gossip exchanges. This advanced approach is expected to make
our model more robust to challenges with insufficient training data, or
mismatched test data. In our simulations, a least-squared problem is considered
to verify the feasibility and effectiveness of AI-based methods. Simulation
results demonstrate that the proposed AI-based methods are beneficial to
improve performance of detecting and localizing malicious agents over
score-based methods, and the peer-to-peer neural network model is indeed robust
to target issues.
