FedZeN: Towards superlinear zeroth-order federated learning via incremental Hessian estimation
This work addresses federated learning for convex optimization in scenarios where derivatives are unavailable, offering a novel method with superlinear convergence, though it is incremental in adapting existing Hessian estimation techniques.
The authors tackled the problem of federated learning when only function evaluations are available, by designing FedZeN, the first federated zeroth-order algorithm that estimates curvature to achieve superlinear convergence, with numerical simulations confirming it outperforms existing methods.
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.