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We study a multi-objective multi-armed bandit problem in a dynamicenvironment. The problem portrays a decision-maker that sequentially selects anarm from a given set. If selected, each action produces a reward vector, whereevery element follows a piecewise-stationary Bernoulli distribution. The agentaims at choosing an arm among the Pareto optimal set of arms to minimize itsregret. We propose a Pareto generic upper confidence bound (UCB)-basedalgorithm with change detection to solve this problem. By developing theessential inequalities for multi-dimensional spaces, we establish that ourproposal 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 formulatean energy-efficient waveform design problem in an integrated communication andsensing system as a toy example. Numerical experiments on the toy example andsynthetic and real-world datasets demonstrate the efficiency of our policycompared to the current methods.

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