Action-Coordinate World Models for Precise Control From Offline Data

World models are trained to predict and then used to plan. Where the task demands precision, the two objectives come apart: a model that fits its observations can still leave the planner without a route to the target. World models are trained to predict and then used to plan. Where the task demands precision, the two objectives come apart: a model that fits its observations can still leave the planner without a route to the target. We study tasks in which objects have to be placed precisely to maximize a signal, although their positions are never observed directly and a context both displaces them and distorts every movement. For them, we introduce action-coordinates, latent representations in which actions act linearly and the target sits at the origin, and build a world model architecture on top of them that moves structure from the planner into the representation. Our theory gives conditions under which action-coordinates exist, the structure they impose, and when they can be learned from high-dimensional observations, together with a closed-form policy and conditions under which it is optimal. On challenging benchmarks of high-fidelity, visually observed tasks, action-coordinate world models outperform planner-based and gradient-based world models and confirm the assumptions of our theory.