  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.
