丛林中的协作学习（去中心化，拜占庭，异构，异步和非凸学习）
Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)
摘要：
我们研究拜占庭协作学习，其中$n$节点寻求从彼此的本地数据中集体学习。数据分布可以从一个节点到另一个节点而变化。没有任何节点是可信的，并且$f < n$节点可以任意行为。我们证明了合作学习等价于一种新的协议形式，我们称之为平均协议。在这个问题中，每个节点都从一个初始向量开始，并试图近似地同意一个共同的向量，这个向量接近诚实节点的初始向量的平均值。我们提出了两个异步的解决方案，平均协议，我们证明每个最佳根据一些维度。第一，基于最小直径平均，需要$ n \geq 6f+1$，但实现渐近最佳可能的平均常数的乘法常数。第二种方法基于可靠广播和坐标修剪均值，实现了最佳拜占庭弹性，即，$n \geq 3f+1$。这些算法中的每一个都导出了一个最优的拜占庭协作学习协议。特别是，我们的等价性产生了新的不可能性定理，任何协作学习算法可以在对抗和异构环境中实现。
英文摘要：
We study Byzantine collaborative learning, where $n$ nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and $f < n$ nodes can behave arbitrarily. We prove that collaborative learning is equivalent to a new form of agreement, which we call averaging agreement. In this problem, nodes start each with an initial vector and seek to approximately agree on a common vector, which is close to the average of honest nodes' initial vectors. We present two asynchronous solutions to averaging agreement, each we prove optimal according to some dimension. The first, based on the minimum-diameter averaging, requires $ n \geq 6f+1$, but achieves asymptotically the best-possible averaging constant up to a multiplicative constant. The second, based on reliable broadcast and coordinate-wise trimmed mean, achieves optimal Byzantine resilience, i.e., $n \geq 3f+1$. Each of these algorithms induces an optimal Byzantine collaborative learning protocol. In particular, our equivalence yields new impossibility theorems on what any collaborative learning algorithm can achieve in adversarial and heterogeneous environments.
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