We study a multi-objective multi-armed bandit problem in a dynamic environment. The problem portrays a decision-maker that sequentially selects an arm from a given set. If selected, each action produces a reward vector, where every element follows a piecewise-stationary Bernoulli distribution. The agent aims at choosing an arm among the Pareto optimal set of arms to minimize its regret. We propose a Pareto generic upper confidence bound (UCB)-based algorithm with change detection to solve this problem. By developing the essential inequalities for multi-dimensional spaces, we establish that our proposal guarantees a regret bound in the order of $\gamma_T\log(T/{\gamma_T})$ when the number of breakpoints $\gamma_T$ is known. Without this assumption, the regret bound of our algorithm is $\gamma_T\log(T)$. Finally, we formulate an energy-efficient waveform design problem in an integrated communication and sensing system as a toy example. Numerical experiments on the toy example and synthetic and real-world datasets demonstrate the efficiency of our policy compared to the current methods.

翻译：本文研究动态环境下的多目标多臂赌博机问题。该问题描述了一个决策者从给定集合中依次选择一支手臂。若被选中，每个动作会产生一个奖励向量，其中每个元素服从分段平稳的伯努利分布。智能体的目标是从帕累托最优手臂集合中选择一支手臂以最小化其遗憾。我们提出了一种带有变化检测的帕累托通用置信上界（UCB）算法来解决该问题。通过推导多维空间中的关键不等式，我们证明了当断点数量$\gamma_T$已知时，该算法能够保证遗憾界为$\gamma_T\log(T/{\gamma_T})$量级。若无此假设，算法的遗憾界为$\gamma_T\log(T)$。最后，我们将集成通信与感知系统中的节能波形设计问题构建为一个玩具示例。在玩具示例、合成数据集和真实数据集上的数值实验表明，与现有方法相比，我们的策略具有高效性。