Scalable Distributed Optimization of Multi-Dimensional Functions Despite Byzantine Adversaries
arXiv (Cornell University)(2024)
摘要
The problem of distributed optimization requires a group of networked agents
to compute a parameter that minimizes the average of their local cost
functions. While there are a variety of distributed optimization algorithms
that can solve this problem, they are typically vulnerable to "Byzantine"
agents that do not follow the algorithm. Recent attempts to address this issue
focus on single dimensional functions, or assume certain statistical properties
of the functions at the agents. In this paper, we provide two resilient,
scalable, distributed optimization algorithms for multi-dimensional functions.
Our schemes involve two filters, (1) a distance-based filter and (2) a min-max
filter, which each remove neighborhood states that are extreme (defined
precisely in our algorithms) at each iteration. We show that these algorithms
can mitigate the impact of up to F (unknown) Byzantine agents in the
neighborhood of each regular agent. In particular, we show that if the network
topology satisfies certain conditions, all of the regular agents' states are
guaranteed to converge to a bounded region that contains the minimizer of the
average of the regular agents' functions.
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关键词
Byzantine attacks,convex optimization,distributed algorithms,fault tolerance,graph theory,machine learning,multi-agent systems,network security
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