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.

翻译：联邦优化作为一种新兴范式，在联邦学习等实际应用中得到广泛部署，使多个客户端（如边缘设备）能够协同优化全局函数。客户端无需共享本地数据集，通常仅需交换本地梯度信息。然而，在许多联邦优化应用中梯度信息难以获取，由此催生了联邦零阶优化（ZOO）范式。现有联邦零阶优化算法存在查询与通信效率低下的局限性，其根源在于：（a）梯度估计需要大量函数查询；（b）实际本地更新与预期全局更新之间存在显著偏差。针对此问题，我们提出：（a）引入轨迹感知梯度代理，该技术可利用优化过程中历史函数查询记录实现精确且查询高效的梯度估计；（b）基于这些梯度代理开发自适应梯度修正技术以缓解上述偏差。基于上述技术，我们提出基于轨迹感知代理梯度的联邦零阶优化（FZooS）算法，实现了查询高效与通信高效的联邦零阶优化。理论分析与联邦黑盒对抗攻击、联邦不可微度量优化等实际实验共同证实，FZooS算法相较现有方法具有显著理论优势。