Federated Zeroth-Order Optimization using Trajectory-Informed Surrogate Gradients

TL;DR

This paper introduces FZooS, a novel federated zeroth-order optimization algorithm that leverages trajectory-informed surrogate gradients to improve query and communication efficiency in scenarios lacking gradient information.

Contribution

It proposes a new gradient surrogate method and adaptive gradient correction technique, significantly enhancing efficiency over existing federated zeroth-order optimization algorithms.

Findings

FZooS outperforms existing methods in query efficiency.

FZooS reduces communication overhead in federated settings.

Demonstrated effectiveness in real-world tasks like black-box attacks.

Abstract

Federated optimization, an emerging paradigm which finds wide real-world applications such as federated learning, enables multiple clients (e.g., edge devices) to collaboratively optimize a global function. The clients do not share their local datasets and typically only share their local gradients. However, the gradient information is not available in many applications of federated optimization, which hence gives rise to the paradigm of federated zeroth-order optimization (ZOO). Existing federated ZOO algorithms suffer from the limitations of query and communication inefficiency, which can be attributed to (a) their reliance on a substantial number of function queries for gradient estimation and (b) the significant disparity between their realized local updates and the intended global updates. To this end, we (a) introduce trajectory-informed gradient surrogates which is able to use the history of function queries during optimization for accurate and query-efficient gradient estimation, and (b) develop the technique of adaptive gradient correction using these gradient surrogates to mitigate the aforementioned disparity. Based on these, we propose the federated zeroth-order optimization using trajectory-informed surrogate gradients (FZooS) algorithm for query- and communication-efficient federated ZOO. Our FZooS achieves theoretical improvements over the existing approaches, which is supported by our real-world experiments such as federated black-box adversarial attack and federated non-differentiable metric optimization.