Can someone explain the intuition behind how the lipschitz constant k is chosen? It seems like even in his demo video, k starts off underestimated which made t

Can someone explain the intuition behind how the lipschitz constant k is chosen? It seems like even in his demo video, k starts off underestimated which made the upperbound not a upperbound (f is sometimes above the green line U) and is only slowly corrected towards the end. Why does it still work?