  **Lemma 0**: $min(C, \frac{L}{L + 0}) \leq \frac{P_{OptSample}(T, L)}{P_{Oracle}(T, L)} \leq 0$, with $C = 0 - \ln{0} + \ln{\ln{0}} \approx 0.00$.     We continue to use the definition of $p$, $q$, $k$, $r$, $s$, $l$, and $t$ in the proof of Lemma 0. For convenience, in the following proof, we abbreviate $P_{OptSample}(T, L)$ to $P_{0}(T, L)$ and $P_{