Establish whether EqC approximation-error terms are small in practice

Determine whether the conditional action-dispersion term σact and the bridge-scale recovery term σscale are small for Equilibrium Energy Control (EqC) on the selected datasets and trained policies, thereby assessing the practical validity of the conditional-concentration regime motivating the stationary-energy approximation.

Background

Appendix C derives an approximation bound for the stationary energy field used by EqC. The bound depends on σact, which measures residual expert-action variation after conditioning on the policy condition, and σscale, which measures how accurately the bridge-dependent scale can be recovered from the current state and condition.

The paper notes that empirical findings motivating the conditional-concentration regime do not establish that these quantities are small for EqC. Direct diagnostics on the selected datasets and trained policies are therefore needed to determine whether the theoretical approximation bound is practically informative in the reported settings.