One note of caution—although it is neat to be able to bound loss, one can still question how useful meaningful ‘loss’ is here. Looking instead at utility, there is no bound on how much worse a quantilizer can perform relative to a random actor (nor how much it would contribute to our regret).
The real reason to use a quantilizer is that we expect that edge cases might have regret on the order of the cosmic endowment, but that most quantilized actions will not. For this thing that matters, there are no guarantees.
The quantilizer idea seems excellent.
One note of caution—although it is neat to be able to bound loss, one can still question how useful meaningful ‘loss’ is here. Looking instead at utility, there is no bound on how much worse a quantilizer can perform relative to a random actor (nor how much it would contribute to our regret).
The real reason to use a quantilizer is that we expect that edge cases might have regret on the order of the cosmic endowment, but that most quantilized actions will not. For this thing that matters, there are no guarantees.