Cover meets Robbins while Betting on Bounded Data: $\ln n$ Regret and Almost Sure $\ln\ln n$ Regret

ArXi:2604.20172v1 Announce Type: new Consider betting against a sequence of data in $[0,1]$, where one is allowed to make any bet that is fair if the data have a conditional mean $m_0 \in (0,1)$. Cover's universal portfolio algorithm delivers a worst-case regret of $O(\ln n)$ compared to the best constant bet in hindsight, and this bound is unimprovable against adversarially generated data.