An improved regret analysis for UCB-N and TS-N
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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 log_2(α) + 3 for α the independence number of the feedback graph.
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