Assume $R$ is Gaussian random variable. I read this from a paper,$\newcommand{var}{\text{Var}}$
$\mathbb{E}[1-\exp\{-\lambda R\}] = 1-\exp\{-\lambda \mathbb{E}(R) + \frac{\lambda^2}{2}\var(R)\}$
and,$\newcommand{argmax}{\text{arg max}}$
$\argmax_{a} 1-\exp\{-\lambda \mathbb{E}(R) + \frac{\lambda^2}{2}Var(R)\} = \argmax_a \mathbb{E}(R) - \frac{\lambda}{2}\var(R)$
where $a$ is a parameter in $R$.
I didn't figure out the derivation steps. Could you please give me some hints on how to get this? Thanks!