In Note 1, if the KL divergence for some distribution is of order $\Delta$, instead of $\Delta^2$ like the Gaussian case, or more general, of order $\Delta^\alpha$, will the lower bound change? ]]>

However, after the correction, there still exists a flaw in the final distribution-free bound for UCB. This bound also requires the suboptimality gaps be bounded, right?

]]>Thanks for pointing out the bugs!

Tor

]]>Also, in the UCB regret (3), should the last constant be ‘1’, but not ‘3’?

Thank you!

]]>After equation (7) “An easy way to avoid numerical instability is to incrementally calculate $$\tilde S_{ti}=\hat S_{ti}–min_j \hat S_{ti}$$…” – should it not be $$\tilde S_{ti}=\hat S_{ti}–min_j \hat S_{tj}$$?

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