Epistemic Action Quotients: A Theory of Consequence-Based Action Abstraction

When should physically different sensing actions be treated as the same? We argue that the answer depends on what the robot needs to learn rather than on how the actions move it. We introduce Epistemic Action Quotients (EAQs), which define action identity through task-conditioned epistemic consequences: two actions are exactly equivalent for a demand when they induce the same distribution over task-projected belief updates. For finite data, we use bounded-diameter operational partitions and establish a Lipschitz within-block regret bound together with a sufficient stability condition under bounded drift. In the tested HM3D and Habitat settings, epistemic identity repeatedly differs from motor similarity and changes with the demand; a sensor pan and a whole-body yaw fall into the same class in all 20 seeds. In a controlled planning study, evaluating one representative per class reduces the candidate set eightfold with no observed regret. We further instantiate Online EAQ, which predicts action consequences from locally available pre-action information and treats demand changes as mandatory refresh events. In an HM3D pilot, task-triggered refresh accounts for most of the improvement over static caching, while all 25 transitions satisfying the realized-branch analogue of $2{\eta }_t<{\rho }_t$ preserve the reference partition.