Which Mutual-Information Representation Learning Objectives are Sufficient for Control?
This work addresses a theoretical gap in representation learning for RL, identifying limitations in existing mutual-information objectives that could impact practitioners designing efficient learning algorithms.
The paper formalizes the sufficiency of state representations for learning optimal policies in reinforcement learning and analyzes mutual-information objectives, finding that two popular ones can yield insufficient representations under common MDP assumptions, with empirical validation on a simulated game environment.
Mutual information maximization provides an appealing formalism for learning representations of data. In the context of reinforcement learning (RL), such representations can accelerate learning by discarding irrelevant and redundant information, while retaining the information necessary for control. Much of the prior work on these methods has addressed the practical difficulties of estimating mutual information from samples of high-dimensional observations, while comparatively less is understood about which mutual information objectives yield representations that are sufficient for RL from a theoretical perspective. In this paper, we formalize the sufficiency of a state representation for learning and representing the optimal policy, and study several popular mutual-information based objectives through this lens. Surprisingly, we find that two of these objectives can yield insufficient representations given mild and common assumptions on the structure of the MDP. We corroborate our theoretical results with empirical experiments on a simulated game environment with visual observations.