We consider the problem of distributed inference where agents in a network observe a stream of private signals generated by an unknown state, and aim to uniquely identify this state from a finite set of hypotheses. We focus on scenarios where communication between agents is costly, and takes place over channels with finite bandwidth. To reduce the frequency of communication, we develop a novel event-triggered distributed learning rule that is based on the principle of diffusing low beliefs on each false hypothesis. Building on this principle, we design a trigger condition under which an agent broadcasts only those components of its belief vector that have adequate innovation, to only those neighbors that require such information. We prove that our rule guarantees convergence to the true state exponentially fast almost surely despite sparse communication, and that it has the potential to significantly reduce information flow from uninformative agents to informative agents. Next, to deal with finite-precision communication channels, we propose a distributed learning rule that leverages the idea of adaptive quantization. We show that by sequentially refining the range of the quantizers, every agent can learn the truth exponentially fast almost surely, while using just $1$ bit to encode its belief on each hypothesis. For both our proposed algorithms, we rigorously characterize the trade-offs between communication-efficiency and the learning rate.

中文翻译：

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具有稀疏和量化通信的分布式推理

我们考虑分布式推理问题，其中网络中的代理观察由未知状态生成的私有信号流，并旨在从有限的假设集中唯一地识别该状态。我们专注于代理之间的通信成本高昂的场景，并且发生在带宽有限的通道上。为了减少交流的频率，我们开发了一种新的事件触发分布式学习规则，该规则基于对每个错误假设的低置信度的扩散原则。基于此原则，我们设计了一个触发条件，在该条件下，代理仅向需要此类信息的邻居广播其信念向量中具有足够创新的那些组件。我们证明，尽管通信稀疏，但我们的规则几乎可以肯定地保证以指数方式快速收敛到真实状态，并且它有可能显着减少从无信息代理到信息代理的信息流。接下来，为了处理有限精度的通信信道，我们提出了一种利用自适应量化思想的分布式学习规则。我们表明，通过连续细化量化器的范围，每个代理几乎可以肯定地以指数方式快速学习真理，同时仅使用 $1$ 位来编码其对每个假设的信念。对于我们提出的两种算法，我们严格描述了通信效率和学习率之间的权衡。接下来，为了处理有限精度的通信信道，我们提出了一种利用自适应量化思想的分布式学习规则。我们表明，通过连续细化量化器的范围，每个代理几乎可以肯定地以指数方式快速学习真理，同时仅使用 $1$ 位来编码其对每个假设的信念。对于我们提出的两种算法，我们严格描述了通信效率和学习率之间的权衡。接下来，为了处理有限精度的通信信道，我们提出了一种利用自适应量化思想的分布式学习规则。我们表明，通过连续细化量化器的范围，每个代理几乎可以肯定地以指数方式快速学习真理，同时仅使用 $1$ 位来编码其对每个假设的信念。对于我们提出的两种算法，我们严格描述了通信效率和学习率之间的权衡。