Tightness of the lookahead bound for closed-loop experimental design

Determine whether the lookahead bound established for open-loop experimental design is tight for a closed-loop designer.

Background

The experimental-design procedure in the paper selects open-loop action sequences and relates the required lookahead to the separating horizon of candidate Regular Decision Processes. For the corridor family, the paper shows that exhaustive open-loop search succeeds when the lookahead reaches the separating depth.

The authors leave unresolved whether an analogous bound is tight when the experiment designer can adapt future actions to observations obtained during the trajectory. A closed-loop designer may exploit intermediate observations and therefore could require less lookahead than the open-loop construction, but the paper does not determine this.