Distributed Online Optimization with Byzantine Adversarial Agents
This addresses the challenge of robust optimization in distributed systems with adversarial agents, which is incremental as it builds on existing online optimization methods by incorporating Byzantine fault tolerance.
The paper tackles the problem of distributed online optimization in multi-agent systems with Byzantine adversarial agents, where non-faulty agents update states using local and neighbor information without prior knowledge of faulty identities, and shows that under certain conditions, the regret grows sublinearly compared to an offline version.
We study the problem of non-constrained, discrete-time, online distributed optimization in a multi-agent system where some of the agents do not follow the prescribed update rule either due to failures or malicious intentions. None of the agents have prior information about the identities of the faulty agents and any agent can communicate only with its immediate neighbours. At each time step, a locally Lipschitz strongly convex cost function is revealed locally to all the agents and the non-faulty agents update their states using their local information and the information obtained from their neighbours. We measure the performance of the online algorithm by comparing it to its offline version, when the cost functions are known apriori. The difference between the same is termed as regret. Under sufficient conditions on the graph topology, the number and location of the adversaries, the defined regret grows sublinearly. We further conduct numerical experiments to validate our theoretical results.