Byzantine Fault-Tolerance in Decentralized Optimization under Minimal Redundancy

This paper considers the problem of Byzantine fault-tolerance in multi-agent decentralized optimization. In this problem, each agent has a local cost function. The goal of a decentralized optimization algorithm is to allow the agents to cooperatively compute a common minimum point of their aggregate cost function. We consider the case when a certain number of agents may be Byzantine faulty. Such faulty agents may not follow a prescribed algorithm, and they may share arbitrary or incorrect information with other non-faulty agents. Presence of such Byzantine agents renders a typical decentralized optimization algorithm ineffective. We propose a decentralized optimization algorithm with provable exact fault-tolerance against a bounded number of Byzantine agents, provided the non-faulty agents have a minimal redundancy.