Threshold-policy entropy optimality conjecture in the special case

In the special case, policies choose observation processes based on the information state, and the performance of a policy is measured by its limiting expected entropy. A threshold policy is a policy whose choice of observation process changes at a threshold in the information-state space.

Threshold-policy entropy optimality conjecture. In the special case, the infimum of entropy attainable under threshold policies is the same as that under general policies.

Numerical searches over locally optimal truncated policies found no policy with lower entropy than the best threshold policy and therefore provide heuristic evidence for the conjecture, but do not prove equality of the two infima.