As the network scale increases, existing fully distributed solutions start to
lag behind the real-world challenges such as (1) slow information propagation,
(2) network communication failures, and (3) external adversarial attacks. In
this paper, we focus on hierarchical system architecture and address the
problem of non-Bayesian learning over networks that are vulnerable to
communication failures and adversarial attacks. On network communication, we
consider packet-dropping link failures.
We first propose a hierarchical robust push-sum algorithm that can achieve
average consensus despite frequent packet-dropping link failures. We provide a
sparse information fusion rule between the parameter server and arbitrarily
selected network representatives. Then, interleaving the consensus update step
with a dual averaging update with Kullback-Leibler (KL) divergence as the
proximal function, we obtain a packet-dropping fault-tolerant non-Bayesian
learning algorithm with provable convergence guarantees.
On external adversarial attacks, we consider Byzantine attacks in which the
compromised agents can send maliciously calibrated messages to others
(including both the agents and the parameter server). To avoid the curse of
dimensionality of Byzantine consensus, we solve the non-Bayesian learning
problem via running multiple dynamics, each of which only involves Byzantine
consensus with scalar inputs. To facilitate resilient information propagation
across sub-networks, we use a novel Byzantine-resilient gossiping-type rule at
the parameter server.

基于分层系统架构，解决面临通信故障和对抗攻击的非贝叶斯学习问题，并提出适应分布式网络的算法

网络容错和拜占庭鲁棒的社交学习通过协作层次非贝叶斯学习

Network Fault-tolerant and Byzantine-resilient Social Learning via  Collaborative Hierarchical Non-Bayesian Learning

Fully distributed estimation and tracking solutions to large-scale
multi-agent networks suffer slow convergence and are vulnerable to network
failures. In this paper, we aim to speed up the convergence and enhance the
resilience of state estimation and tracking using a simple hierarchical system
architecture wherein agents are clusters into smaller networks, and a parameter
server exists to aid the information exchanges among networks. The information
exchange among networks is expensive and occurs only once in a while.
We propose two consensus + innovation algorithms for the state estimation and
tracking problems, respectively. In both algorithms, we use a novel
hierarchical push-sum consensus component. For the state estimation, we use
dual averaging as the local innovation component. State tracking is much harder
to tackle in the presence of dropping-link failures and the standard
integration of the consensus and innovation approaches are no longer
applicable. Moreover, dual averaging is no longer feasible. Our algorithm
introduces a pair of additional variables per link and ensure the relevant
local variables evolve according to the state dynamics, and use projected local
gradient descent as the local innovation component. We also characterize the
convergence rates of both of the algorithms under linear local observation
model and minimal technical assumptions. We numerically validate our algorithm
through simulation of both state estimation and tracking problems.

本文提出了一种简单的分层系统结构，利用参数服务器对信息交换进行协调，引入创新性的分层推送和局部梯度下降来加速状态估计，特别是在状态跟踪中，我们通过引入额外的变量，使相关的局部变量根据状态动态演化。