A New Approach for Distributed Hypothesis Testing with Extensions to Byzantine-Resilience
A New Approach for Distributed Hypothesis Testing with Extensions to Byzantine-Resilience
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DOI：
10.23919/acc.2019.8815195
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发表时间：
2019-03
期刊：
影响因子：
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通讯作者：
A. Mitra;J. Richards;S. Sundaram
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文献类型：
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作者：
A. Mitra;J. Richards;S. Sundaram
我们研究了这样一种设置，其中一组代理，每个代理接收部分信息的私人观察，寻求协作学习真实状态（在一组假设中），以解释他们随时间的联合观察概况。为了解决这个问题，我们提出了一种与现有方法根本不同的分布式学习规则，因为它不采用任何形式的“置信平均”。具体来说，每个代理都对每个假设维护一个本地信念，该假设以贝叶斯方式更新，不受任何网络影响，并且实际信念被更新（直到归一化）作为其自己的本地信念和其邻居的实际信念的最小值。在对智能体信号结构和底层通信图的最低要求下，我们建立了所提出的信念更新规则的一致性，即，我们表明智能体的实际信念几乎肯定渐近地集中在真实状态。作为我们方法的主要优点之一，我们表明我们的学习规则可以扩展到捕获网络中某些代理的不当行为的场景，通过拜占庭对手模型进行建模。特别是，我们证明，在观察模型和网络拓扑的适当条件下，每个非对抗性智能体几乎可以肯定地渐进地了解世界的真实状态。
We study a setting where a group of agents, each receiving partially informative private observations, seek to collaboratively learn the true state (among a set of hypotheses) that explains their joint observation profiles over time. To solve this problem, we propose a distributed learning rule that differs fundamentally from existing approaches, in the sense that it does not employ any form of “belief-averaging”. Specifically, every agent maintains a local belief on each hypothesis that is updated in a Bayesian manner without any network influence, and an actual belief that is updated (up to normalization) as the minimum of its own local belief and the actual beliefs of its neighbors. Under minimal requirements on the signal structures of the agents and the underlying communication graph, we establish consistency of the proposed belief update rule, i.e., we show that the actual beliefs of the agents asymptotically concentrate on the true state almost surely. As one of the key benefits of our approach, we show that our learning rule can be extended to scenarios that capture misbehavior on the part of certain agents in the network, modeled via the Byzantine adversary model. In particular, we prove that each non-adversarial agent can asymptotically learn the true state of the world almost surely, under appropriate conditions on the observation model and the network topology.