In this paper, we study a linear bandit optimization problem in a federated
setting where a large collection of distributed agents collaboratively learn a
common linear bandit model. Standard federated learning algorithms applied to
this setting are vulnerable to Byzantine attacks on even a small fraction of
agents. We propose a novel algorithm with a robust aggregation oracle that
utilizes the geometric median. We prove that our proposed algorithm is robust
to Byzantine attacks on fewer than half of agents and achieves a sublinear
$\tilde{\mathcal{O}}({T^{3/4}})$ regret with $\mathcal{O}(\sqrt{T})$ steps of
communication in $T$ steps. Moreover, we make our algorithm differentially
private via a tree-based mechanism. Finally, if the level of corruption is
known to be small, we show that using the geometric median of mean oracle for
robust aggregation further improves the regret bound.

研究在联邦学习环境下的线性赌博机优化问题，提出一个具有鲁棒聚合神谕的新算法，证明该算法对少于一半的代理进行拜占庭攻击是鲁棒的，并通过基于树的机制使算法具有差分隐私。如果已知污染程度较小，则使用平均几何中位数神谕来进行鲁棒聚合进一步改善遗憾界。