Piecewise-Stationary Multi-Objective Multi-Armed Bandit with Application to Joint Communications and Sensing

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 <inline-formula> <tex-math notation="LaTeX">$\gamma _{T}\log (T/{\gamma _{T}})$ </tex-math></inline-formula> when the number of breakpoints <inline-formula> <tex-math notation="LaTeX">$\gamma _{T}$ </tex-math></inline-formula> is known. Without this assumption, the regret bound of our algorithm is <inline-formula> <tex-math notation="LaTeX">$\gamma _{T}\log (T)$ </tex-math></inline-formula>. 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.