A Note on Bounding Regret of the C$^2$UCB Contextual Combinatorial Bandit
arXiv:1902.07500v14 citations
Originality Synthesis-oriented
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This is an incremental correction for researchers in bandit algorithms, ensuring theoretical reliability of prior results.
The paper identifies an error in the proof of bounded regret for the C²UCB contextual combinatorial bandit algorithm and provides a corrected proof to maintain the original regret bound.
We revisit the proof by Qin et al. (2014) of bounded regret of the C$^2$UCB contextual combinatorial bandit. We demonstrate an error in the proof of volumetric expansion of the moment matrix, used in upper bounding a function of context vector norms. We prove a relaxed inequality that yields the originally-stated regret bound.