A Note on Bounding Regret of the C$^2$UCB Contextual Combinatorial Bandit

Oetomo, Bastian, Perera, Malinga, Borovica-Gajic, Renata, Rubinstein, Benjamin I. P.

arXiv.org Machine Learning 

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.