# Gambling

## [UIT 1] Regret bound for mixture method

Summary: Derivation of upper bound on the regret for the mixture method (KT scheme) for individual sequence prediction. Suppose $\mathcal{X} = \{1, \ldots, m\}$ for some integer $m \geq 2$ and let $\Theta = \Delta_m$ denote the $m-1$ dimensional probability simplex.