Distributed Online Optimization with Byzantine Adversarial Agents

TL;DR

This paper addresses distributed online optimization in multi-agent systems with some agents being malicious or failing, proposing algorithms that achieve sublinear regret despite adversarial agents and limited communication.

Contribution

It introduces a novel distributed online optimization algorithm robust to Byzantine adversaries with theoretical guarantees on regret growth.

Findings

Regret grows sublinearly under certain conditions.

Algorithm is robust to malicious agents.

Numerical experiments validate theoretical results.

Abstract

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.