In the setting of stochastic online learning with undirected feedback graphs, Lykouris et al. (2020) previously analyzed the pseudo-regret of the upper confidence bound-based algorithm UCB-N and the Thompson Sampling-based algorithm TS-N. In this note, we show how to improve their pseudo-regret analysis. Our improvement involves refining a key lemma of the previous analysis, allowing a log(T) factor to be replaced by a factor log2(α)+3 for α the independence number of the feedback graph.
@article{arxiv.2305.04093,
title = {An improved regret analysis for UCB-N and TS-N},
author = {Nishant A. Mehta},
journal= {arXiv preprint arXiv:2305.04093},
year = {2023}
}