Open directions in adaptive experiment design and duration optimization

Investigate adaptive multi-input minimum lengths, sharper competitive constants, and experiments that adapt their duration to an unknown time scale.

Background

The paper establishes exact minimum durations for predetermined universal input sequences, showing that the required duration is mn+1 transitions with exact states and m(n+1) transitions with positive sensor uncertainty. It also proves constant-factor competitiveness of the shortest sequences under spectral separation conditions and characterizes the order-1/h duration required for competitiveness in slowly actuated systems of the form A_h=I+hG.

The authors explicitly identify three unresolved directions: determining minimum lengths for adaptive multi-input experiments, improving or characterizing the constants in the competitive bounds, and designing experiments whose duration can adapt when the slow time scale is unknown. These directions extend the paper's fixed-duration, predetermined-sequence results and its analysis of a known time scale.