Review for NeurIPS paper: Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework

Weaknesses: The presentation of the unified framework suffers from some flaws in the mathematical exposition, and could be greatly improved. In particular, the casual presentation of Equation (2) makes it difficult to parse. This casual presentation also (a) does not make it obvious that the later equations (e.g. Eq (3)) are actually bi-level optimization frameworks, which is what makes the contribution of the proposed paper difficult/novel, and (b) makes some of the definitions building off of Eq (2) also imprecise or hard to understand. Please see the "additional feedback" section for specific suggestions as to how to clarify this framework. As this conceptual framework is a major contribution of the paper, it is critical that the authors improve the presentation.