Federated learning is a distributed learning framework that allows a set of
clients to collaboratively train a model under the orchestration of a central
server, without sharing raw data samples. Although in many practical scenarios
the derivatives of the objective function are not available, only few works
have considered the federated zeroth-order setting, in which functions can only
be accessed through a budgeted number of point evaluations. In this work we
focus on convex optimization and design the first federated zeroth-order
algorithm to estimate the curvature of the global objective, with the purpose
of achieving superlinear convergence. We take an incremental Hessian estimator
whose error norm converges linearly, and we adapt it to the federated
zeroth-order setting, sampling the random search directions from the Stiefel
manifold for improved performance. In particular, both the gradient and Hessian
estimators are built at the central server in a communication-efficient and
privacy-preserving way by leveraging synchronized pseudo-random number
generators. We provide a theoretical analysis of our algorithm, named FedZeN,
proving local quadratic convergence with high probability and global linear
convergence up to zeroth-order precision. Numerical simulations confirm the
superlinear convergence rate and show that our algorithm outperforms the
federated zeroth-order methods available in the literature.

本研究使用增量 Hessian 估计器在协同训练集中设计第一个估计全局目标曲率的零阶联邦学习算法，以达到超线性收敛，通过在 Stiefel 流形中对随机搜索方向进行采样以提高性能。我们通过使用同步的伪随机数生成器以一种通信高效和隐私保护的方式，在中央服务器上构建梯度和 Hessian 估计器。我们对我们的算法进行了理论分析，命名为 FedZeN，证明了具有高概率的局部二次收敛和全局线性收敛的零阶精度。数值模拟验证了超线性收敛速率，并表明我们的算法优于文献中可用的零阶联邦学习方法。