Bennett inequality
= Bennett inequality
{c}
{wiki}
If independent centered random variables satisfy $X_i\leq b$ and $\sum_i\mathbb EX_i^2\leq v$, then
$$
\mathbb P\left(\sum_iX_i\geq t\right)
\leq\exp\left[-\frac v{b^2}h\left(\frac{bt}{v}\right)\right],
\qquad h(u)=(1+u)\log(1+u)-u.
$$