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arXiv · 2302.05257

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

Amir Rezaei Balef·Setareh Maghsudi
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Abstract

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.

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Amir Rezaei Balef, Setareh Maghsudi. 2023-02-10. Piecewise-Stationary Multi-Objective Multi-Armed Bandit with Application to Joint Communications and Sensing. https://arxiv.org/abs/2302.05257

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