Calculating the privacy that Renyi ($\epsilon, \delta$) Differential Privacy satisfies
I don't think your interpretation of $\varepsilon$ in DP is correct. You can find a decent explanation of this parameter in this crypto.SE question and links therein.
The best intuition I have for Rényi privacy is that it bounds the average of the privacy loss) $L(O)$: instead of being a worst-case property, like DP (&quot;for all outputs $O$, $L(O)$ is lower than $\varepsilon$&quot;), Rényi privacy is an average-case property (&quot;when we average $L(O)$ across all possible outputs $O$, the result is lower than $\varepsilon$&quot;). The $\alpha$ parameter determines which kind of average we're using: used: $\alpha=1$ bounds the arithmetic mean of $L(O)$, $\alpha=2$ bounds the arithmetic mean of $e^{L(O)}$, $\alpha=3$ bounds the quadratic mean of $e^L(O)$, etc.