As I was doing the "Advanced Combat" quest, everything was fine. However, since I had another quest to look at the pedestals, I got caught into the arena again when I tried to do the other quest. But this time, there was no puppet, and I could not leave. Quitting the game and re-entering seems to fix this, but you still need to do the lesson again. Going to character selection will not fix it.
This happens when you finish fighting the puppet, then before you get the experience, you go back into the area to choose a match, and the game assumes you have't done the quest yet, and puts you back in the arena.