Hierarchical Thompson Sampling for Multi-band Radio Channel Selection

We consider the multi-band channel selection problem, where the best channel is to be selected from $n$ distinct frequency bands, each containing $m$ wireless channels. The objective is to select the channel with the best average signal-to-interference-plus-noise ratio (SiNR), where the SiNR for each channel follows a parametric distribution, generated from a band-dependent prior distribution. We introduce a Bayesian Hierarchical Bandit (BHB) model that captures the correlation induced by the hierarchical relationship between channels and band, and develop a Hierarchical Thompson sampling (HTS) algorithm which leverages the underlying Bayesian Hierarchical structure to efficiently determine which channel is optimal. We demonstrate that the HTS algorithm outperforms traditional bandit algorithms by a factor of $n$ when the bands are sufficiently dissimilar. Through extensive simulation, we characterize the Bayesian regret of the HTS algorithm under varying degrees of band similarity and demonstrate that the Bayesian regret of HTS does not increase linearly with $n$ , in contrast to traditional bandit algorithms.