On the Limited Representational Power of Value Functions and its Links to Statistical (In)Efficiency

Identifying the trade-offs between model-based and model-free methods is a central question in reinforcement learning. Value-based methods offer substantial computational advantages and are sometimes just as statistically efficient as model-based methods. However, focusing on the core problem of policy evaluation, we show information about the transition dynamics may be impossible to represent in the space of value functions. We explore this through a series of case studies focused on structures that arises in many important problems. In several, there is no information loss and value-based methods are as statistically efficient as model based ones. In other closely-related examples, information loss is severe and value-based methods are severely outperformed. A deeper investigation points to the limitations of the representational power as the driver of the inefficiency, as opposed to failure in algorithm design.