From Partial Identification to Directed Exploration in World Models

World models support planning by predicting action consequences, but data collected by a controller may lack sufficient action variation, leaving different predictions for untried actions. We study world models with linear Gaussian latent dynamics and recoverable states. We fully characterize which action effects existing data determine and which remain ambiguous, and quantify how prediction accuracy on observed trajectories constrains predictions under changed actions. This characterization guides the identification of action directions requiring additional exploration. We determine the minimum number of directions needed to resolve the ambiguity and optimize probing strength across these directions to improve the accuracy of action effect estimates. The resulting method combines existing trajectories and new interventions to estimate action effects. We further analyze how errors in learning state representations and selecting probe directions affect the final estimation accuracy. With matched interaction counts and action perturbation budgets, directed acquisition reduces control cost by about 53% against balanced full-space exploration under missing and weak coverage. Robot manipulation and pixel experiments further show improvements in control success and action response prediction, respectively.