Before revision:  With an additional\texttt{  Strong-Law-type assumption, we show that the total number of file fetches under \texttt{LeadCache} remains almost surely finite . Additionally , we derive a tight regret lower bound using results from graph coloring.
After revision:  With an additional\texttt{ Strong-Law-type assumption, we show that the total number of file fetches under \texttt{LeadCache} remains almost surely finite over an infinite horizon. Finally , we derive a tight regret lower bound using results from graph coloring.