Knowledge that there is an action to select, in the form of having an action in hand, allows the implementation of exactly one chooser: The one that always selects that action.
[1] holds for any function k / partition k−1 between any two sets. The proof you want may be that A→B is an exponential space and therefore usually larger than A.
interleave/sandwich should then take two predictions as parameters. This suggests that we could define a metric on the space of predictions, and then sandwich the chooser between two nearby predictions, to measure its response to inaccurate predictions.
Re: the third point, I think it’s important to differentiate between f(k(f)) and t(k(f)), where t is the true prediction, that is what actually happens when an agent performs the action A.
f(k(f)) is simply the outcome the agent is aiming at, while t(k(f)) is the outcome the agent eventually gets. So maybe it’s more interesting a measure of similarity in B, from which you can compare the two.
Knowledge that there is an action to select, in the form of having an action in hand, allows the implementation of exactly one chooser: The one that always selects that action.
[1] holds for any function k / partition k−1 between any two sets. The proof you want may be that A→B is an exponential space and therefore usually larger than A.
interleave/sandwich should then take two predictions as parameters. This suggests that we could define a metric on the space of predictions, and then sandwich the chooser between two nearby predictions, to measure its response to inaccurate predictions.
Re: the third point, I think it’s important to differentiate between f(k(f)) and t(k(f)), where t is the true prediction, that is what actually happens when an agent performs the action A.
f(k(f)) is simply the outcome the agent is aiming at, while t(k(f)) is the outcome the agent eventually gets. So maybe it’s more interesting a measure of similarity in B, from which you can compare the two.