Byzantine-Resilient Resource Allocation Over Decentralized Networks

This paper considers the resource allocation problem over a decentralized multi-agent network and at presence of Byzantine agents. Compared with its centralized counterpart, a decentralized algorithm enjoys better scalability when the network is large-scale, but is more vulnerable when some of the agents are malicious and send wrong messages during the optimization process. We utilize the classical Byzantine attack model to describe these malicious actions, and propose a novel Byzantine-resilient decentralized resource allocation algorithm, abbreviated as BREDA. At each iteration of BREDA, each honest agent receives messages from its neighbors, uses coordinate-wise trimmed mean (CTM) to aggregate these messages, and then updates its local primal and dual variables with gradient descent and ascent, respectively. Theoretical analysis indicates that BREDA converges to a neighborhood of an optimal solution. Numerical experiments demonstrate the resilience of BREDA to various Byzantine attacks.