Federated optimization studies the problem of collaborative function optimization among multiple clients (e.g. mobile devices or organizations) under the coordination of a central server. Since the data is collected separately by each client and always remains decentralized, federated optimization preserves data privacy and allows for large-scale computing, which makes it a promising decentralized machine learning paradigm. Though it is often deployed for tasks that are online in nature, e.g., next-word prediction on keyboard apps, most works formulate it as an offline problem. The few exceptions that consider federated bandit optimization are limited to very simplistic function classes, e.g., linear, generalized linear, or non-parametric function class with bounded RKHS norm, which severely hinders its practical usage. In this paper, we propose a new algorithm, named Fed-GO-UCB, for federated bandit optimization with generic non-linear objective function. Under some mild conditions, we rigorously prove that Fed-GO-UCB is able to achieve sub-linear rate for both cumulative regret and communication cost. At the heart of our theoretical analysis are distributed regression oracle and individual confidence set construction, which can be of independent interests. Empirical evaluations also demonstrate the effectiveness of the proposed algorithm.

翻译：联邦优化研究在中央服务器协调下，多个客户端（如移动设备或组织）协同优化函数的问题。由于数据由各客户端独立收集且始终分散存储，联邦优化既保护了数据隐私，又支持大规模计算，成为极具前景的分布式机器学习范式。尽管此类技术通常部署于在线任务（如键盘应用的下一词预测），现有研究多将其建模为离线问题。少数考虑联邦赌博机优化的方法仅限于极简函数类（如线性、广义线性或RKHS范数有界的非参数函数类），严重制约了实际应用。本文提出新算法Fed-GO-UCB，专为具有通用非线性目标函数的联邦赌博机优化设计。在温和条件下，我们严格证明了Fed-GO-UCB能在累积遗憾和通信成本上实现次线性速率。理论分析的核心在于分布式回归预估器与个体置信区间构造技术，这两项成果具有独立研究价值。实验评估亦验证了所提算法的有效性。