In this paper, we investigate federated contextual linear bandit learning within a wireless system that comprises a server and multiple devices. Each device interacts with the environment, selects an action based on the received reward, and sends model updates to the server. The primary objective is to minimize cumulative regret across all devices within a finite time horizon. To reduce the communication overhead, devices communicate with the server via over-the-air computation (AirComp) over noisy fading channels, where the channel noise may distort the signals. In this context, we propose a customized federated linear bandits scheme, where each device transmits an analog signal, and the server receives a superposition of these signals distorted by channel noise. A rigorous mathematical analysis is conducted to determine the regret bound of the proposed scheme. Both theoretical analysis and numerical experiments demonstrate the competitive performance of our proposed scheme in terms of regret bounds in various settings.

翻译：本文研究了包含一个服务器和多个设备的无线系统中的联邦上下文线性赌博学习问题。每台设备与环境交互，根据收到的奖励选择动作，并将模型更新发送至服务器。主要目标是在有限时间范围内最小化所有设备的累积遗憾。为降低通信开销，设备通过含噪衰落信道中的空中计算（AirComp）与服务器通信，信道噪声可能导致信号失真。在此背景下，我们提出了一种定制化的联邦线性赌博方案，其中每台设备传输模拟信号，服务器接收这些信号受信道噪声扭曲后的叠加结果。通过严格的数学分析确定了该方案的遗憾界。理论分析与数值实验均表明，所提方案在不同设置下的遗憾界具有竞争性能。