Asynchronous Approximate Byzantine Consensus: A Multi-hop Relay Method and Tight Graph Conditions
CoRR(2024)
摘要
We study a multi-agent resilient consensus problem, where some agents are of
the Byzantine type and try to prevent the normal ones from reaching consensus.
In our setting, normal agents communicate with each other asynchronously over
multi-hop relay channels with delays. To solve this asynchronous Byzantine
consensus problem, we develop the multi-hop weighted mean subsequence reduced
(MW-MSR) algorithm. The main contribution is that we characterize a tight graph
condition for our algorithm to achieve Byzantine consensus, which is expressed
in the novel notion of strictly robust graphs. We show that the multi-hop
communication is effective for enhancing the network's resilience against
Byzantine agents. As a result, we also obtain novel conditions for resilient
consensus under the malicious attack model, which are tighter than those known
in the literature. Furthermore, the proposed algorithm can be viewed as a
generalization of the conventional flooding-based algorithms, with less
computational complexity. Lastly, we provide numerical examples to show the
effectiveness of the proposed algorithm.
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