I am trying to solve the probability approximately correct learning problem and encountered the inequality, where $Z_i$ are i.i.d. random variables with range $0\leq Z_i \leq 1$ $$\Pr \left( \sum_{i=1}^n \frac{1}{n} (Z_i-\mathbb{E}Z_i)>\varepsilon \right) \leq \exp\left( \frac{-n\varepsilon^2}{2(\varepsilon/3+\mathbb{E}Z_i)} \right) $$ which required me to proved a concentration inequality with expectation at denominator. However, the Chernoff bound have expectation in numerator. May anyone give me some hints where to start?
2026-04-02 10:00:31.1775124031
Concentration inequality involved the mean in RHS denominator
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