__ Summary and Contributions__: Authors presented two novel methods for leaning models in SMDP using neural ODE. Their method can model continuous time environment which can be further used to learn policies. Additionally, authors compared their methods with baselines and showed a significant gain in performance.

__ Strengths__: 1. Novelty : I believe the strongest part of the paper is its novelty. Using neural ODE to learn SMDP is novel to the best of my knowledge. And tackling the SMDPs are really important as they are often the case specially in HC cases.
2. Writing : I found the paper very easy to follow and well motivated.

__ Weaknesses__: I think the paper can significantly benefit from an experiment in a larger state space setting. As one of my main concerns is the scalability of using neuralODE for a more sophisticated environments, mainly larger state space.
Transferring to environments with different time schedules : This has been mentioned, and emphasized, but I believe there should be an example of a case where this doesn't hold, they mention Atari, but I would like to see an experiment when this doesn't hold.

__ Correctness__: Yes.

__ Clarity__: I believe the paper is well written.

__ Relation to Prior Work__: Yes

__ Reproducibility__: Yes

__ Additional Feedback__: I do wonder what is the application of this in off-policy setting, when you have irregular samples of actions. for example in HC setting and ICU, you'll probably have irregular samples of vital signs, or actions. I would appreciate a comment on that.
## After reading author's feedback I keep my score as it was.

__ Summary and Contributions__: The paper proposes a method for utilizing ODEs to represent dynamics for continuous-time decision-making problems with the aim of
They also target filling a perceived gap in the literature of Deep RL for continuous-time problems, where most publications are model-free and discretize time if it is continuous. They claim that their approach leads to lower dependence on vast amounts of training data, better performance and that the model-based approach is well-founded. I tend to agree, although this is not exactly my area.
I also believe the importance of connecting ODEs and other explicit models is critical for extending RL methods to important problems in physics, chemistry, epidemiology and population modelling.

__ Strengths__: Their use of Neural ODEs seems novel but that is a recently introduced model so it is not surprising.
The writing is very clear and the models are described in sufficient detail to be reproduced. Their experimental design and methodology is very nicely done, with increasing complexity of domains that match their claims.

__ Weaknesses__: What they fail to seriously justify or distinguish is why the specific method of Neural ODEs are necessary. It's not even entirely convincing that their use differs from the use of ODEs to define the problem dynamics directly from the RL point of view. There are many papers on using RL to solve ODE problems, isn't any approach that attempts to learn a transition distribution where the simulator or dynamics are based upon ODEs actually a competitor here?

__ Correctness__: Something I find unclear is the role of the latent state z and which parts of the system have access to it. It would be natural to say that the simulator is defined by an ODE, which is unknown to the agent and z is the model approximation that the agent is learning on top of their value function. But the discussion of learning the approximation model P doesn't give me confidence about that separation?
does the agent ever have access to z itself or is this a true hidden state from agent's point of view?
If the agent is not learning the model P then what does it matter that the ODE underlying it's experience is the "true" ODE from the simulator vs the learned neural ODE?

__ Clarity__: The paper is very well written and each part is clearly described. There are some issues with clarity and motivation at a larger level which I have already commented on in other sections.

__ Relation to Prior Work__: The related literature which is discussed is done well. I think an additional connection to RL approaches to solving ODE problems is very relevant.

__ Reproducibility__: No

__ Additional Feedback__: The rebuttal is appreciated and does clarify things somewhat.
My overall review has not changed.

__ Summary and Contributions__: This paper proposed to model the continuous-time dynamics of the semi-Markov decision process (SMDP) via neural ordinary differential equations.
Experiments across various continuous-time domains demonstrate the efficacy of the proposed methods.

__ Strengths__: 1) The proposed method incorporate action and time into the neural ODE framework to model the continuous-time dynamics of the semi-Markov decision process (SMDP), which is theoretically sound and overcomes shortcomings of existing neural ODEs.
2) Detailed experiments on continuous-time domains demonstrates the superiority of the proposed method in terms of model learning, planning, and robustness for changes in interval times.

__ Weaknesses__: It would be better to extend the x-axis of Fig 4 to longer environment steps to illustrate the performance more clearly. For example, the reward of the latent-ODE in the Swimmer plot seems to decrease at the end of the x-axis, while that of the delta-t RNN is shown to be increasing.

__ Correctness__: No explicit incorrect statements.

__ Clarity__: The paper is written clearly.

__ Relation to Prior Work__: Yes.

__ Reproducibility__: Yes

__ Additional Feedback__: I have read the rebuttal and the author has addressed the issue regarding experiments.