Characterize the relative informativeness of quality and preference feedback

Identify minimal structural conditions on the distribution family and reward model p_theta,r_theta that determine whether deterministic pointwise quality feedback is more informative than pairwise preference feedback, less informative, or statistically equivalent.

Background

The paper establishes that pointwise quality labels and pairwise preferences can be incomparable: pointwise labels yield fast localization in some models where preferences provide no localization, while preferences can be more informative in models where pointwise labels are uninformative. The unresolved issue is to determine general structural criteria governing these different informational relationships.

The requested characterization would extend the paper's distribution-specific separation examples into a general theory of when each feedback modality improves parameter estimation.