a.k.a. McDiarmid's inequality

Let $Z_1,...,Z_m \in \mathcal{Z}$ (remember for random variables $\in$ is interpreted as they take values in, or the codomain of the r.v. is ) be $m$ i.i.d. Random variables, and let $h: \mathcal{Z}^m \to \mathbb{R}$ be a function satisfying, for every $k \in \{1,...,m\}$ and for all $z_1,...,z_m,z'_k \in \mathcal{Z}$:

$|h(z_1,...,z_{k-1},z_k,z_{k+1},...,z_m) - h(z_1,...,z_{k-1},z_k,z'_{k+1},...,z_m)| \leq c$

so changing any of the arguments of $h$ doesn't change the output much.. Then,

$\mathbf{P}(h(Z_1,...,Z_m) \geq \mathbf{E}h(Z_1,...,Z_m)+t) \leq \exp{\left(-\frac{2t^2}{mc^2}\right)}$

or, equivalently, with probability at least $1-\delta$ we have

$h(Z_1,...,Z_m) \leq \mathbf{E}h(Z_1,...,Z_m) + c\sqrt{\frac{m}{2}\log{\frac{1}{\delta}}}$

See version using variance here