On the Sensory Commutativity of Action Sequences for Embodied Agents

We study perception in the scenario of an embodied agent equipped with first-person sensors and a continuous motor space with multiple degrees of freedom. Inspired by two theories of perception in artificial agents (Higgins (2018), Poincar\'e (1895)) we consider theoretically the commutation properties of action sequences with respect to sensory information perceived by such embodied agent. From the theoretical derivations, we define the Sensory Commutativity Probability criterion which measures how much an agent's degree of freedom affects the environment in embodied scenarios. We empirically illustrate how it can be used to improve sample-efficiency in Reinforcement Learning.