Piecewise-Stationary Multi-Objective Multi-Armed Bandit with Application to Joint Communications and Sensing
This work addresses decision-making in dynamic multi-objective settings, with applications like joint communications and sensing, representing an incremental advancement in bandit algorithms.
The paper tackles a multi-objective multi-armed bandit problem in a dynamic environment with piecewise-stationary reward distributions, proposing a Pareto UCB-based algorithm with change detection that achieves regret bounds of order γ_T log(T/γ_T) when breakpoints are known and γ_T log(T) otherwise, as validated by numerical experiments on synthetic and real-world datasets.
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 $γ_T\log(T/{γ_T})$ when the number of breakpoints $γ_T$ is known. Without this assumption, the regret bound of our algorithm is $γ_T\log(T)$. 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.