Review for NeurIPS paper: Minimax Regret of Switching-Constrained Online Convex Optimization: No Phase Transition

Additional Feedback: Can you explain more what is the reason for the disappearance of the phase transition compared to the discrete game? In the discrete game without a switching bound, you would typically get a total cost of (1 epsilon)*OPT (log n)/epsilon, and then set epsilon sqrt((log n)/T) to balance the losses. This means that even without a switching bound, against an oblivious adversary, you're switching between actions only about 1/sqrt(T) of the time anyway. On the other hand, you are constantly modifying your probability distribution every round (just that this change is only occasionally reflected in a switch of actions). In your game, there isn't this distinction between the hidden probability distribution and the action played. Is that partly the difference?