Large offline learning-based models have enabled robots to successfully interact with objects for a wide variety of tasks. However, these models rely on fairly consistent structured environments. For more unstructured environments, an online learning component is necessary to gather and estimate information about objects in the environment in order to successfully interact with them. Unfortunately, online learning methods like Bayesian non-parametric models struggle with changes in the environment, which is often the desired outcome of interaction-based tasks. We propose using an object-centric representation for interactive online learning. This representation is generated by transforming the robot's actions into the object's coordinate frame. We demonstrate how switching to this task-relevant space improves our ability to reason with the training data collected online, enabling scalable online learning of robot-object interactions. We showcase our method by successfully navigating a manipulator arm through an environment with multiple unknown objects without violating interaction-based constraints.