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 This paper is a combination of two main and only vaguely related parts: one is a set of theoretical results regarding the existence of policy gradients for MDPs with deterministic (or mixed deterministic and stochastic) state transitions, and the other one is a new algorithm (GDPB) combining model-free and model-based policy gradients. The theoretical results seem to me like they further the understanding of DPG. This is more clearly the case for the negative result. For the mixture-of-deterministic-and-stochastic-transitions result, however, I might be missing something but I don’t see how the way that the two models are combined does not simply produce a stochastic transition model. Even disregarding this, I am not sure the particular combination of transition models they look at is that relevant for real-world tasks - for me it would be much more important to deal with the setting where some state features have deterministic transitions and others do not. I would have liked to see a more in-depth discussion of the model-based approach, in particular using the upper-bounded model-based value functions, as it seems like it could be a promising general technique. One thing that wasn’t clear to me was why the improvement in the lower-bound objective guarantees an improvement in the original objective, which seems like a key argument. The empirical results look reasonable, although I am always a bit suspicious of introducing a new parameter (alpha in this case) that is tuned using the benchmark domains. In summary, I would have given this paper a higher rating if I had been convinced of either the real-world relevance of their positive theoretical result, or the generality of the GDPG algorithm. One minor comment is that the * subscript notation is a bit confusing, as * is typically used for the optimal value / policy.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
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user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 This paper is a combination of two main and only vaguely related parts: one is a set of theoretical results regarding the existence of policy gradients for MDPs with deterministic (or mixed deterministic and stochastic) state transitions, and the other one is a new algorithm (GDPB) combining model-free and model-based policy gradients. The theoretical results seem to me like they further the understanding of DPG. This is more clearly the case for the negative result. For the mixture-of-deterministic-and-stochastic-transitions result, however, I might be missing something but I don’t see how the way that the two models are combined does not simply produce a stochastic transition model. Even disregarding this, I am not sure the particular combination of transition models they look at is that relevant for real-world tasks - for me it would be much more important to deal with the setting where some state features have deterministic transitions and others do not. I would have liked to see a more in-depth discussion of the model-based approach, in particular using the upper-bounded model-based value functions, as it seems like it could be a promising general technique. One thing that wasn’t clear to me was why the improvement in the lower-bound objective guarantees an improvement in the original objective, which seems like a key argument. The empirical results look reasonable, although I am always a bit suspicious of introducing a new parameter (alpha in this case) that is tuned using the benchmark domains. In summary, I would have given this paper a higher rating if I had been convinced of either the real-world relevance of their positive theoretical result, or the generality of the GDPG algorithm. One minor comment is that the * subscript notation is a bit confusing, as * is typically used for the optimal value / policy.
assistant
 This paper is a combination of two main and only vaguely related parts: one is a set of theoretical results regarding the existence of policy gradients for MDPs with deterministic (or mixed deterministic and stochastic) state transitions, and the other one is a new algorithm (GDPB) combining model-free and model-based policy gradients. The theoretical results seem to me like they further the understanding of DPG. This is more clearly the case for the negative result. For the mixture-of-deterministic-and-stochastic-transitions result, however, I might be missing something but I don’t see how the way that the two models are combined does not simply produce a stochastic transition model. Even disregarding this, I am not sure the particular combination of transition models they look at is that relevant for real-world tasks - for me it would be much more important to deal with the setting where some state features have deterministic transitions and others do not. I would have liked to see a more in-depth discussion of the model-based approach, in particular using the upper-bounded model-based value functions, as it seems like it could be a promising general technique. One thing that wasn’t clear to me was why the improvement in the lower-bound objective guarantees an improvement in the original objective, which seems like a key argument. The empirical results look reasonable, although I am always a bit suspicious of introducing a new parameter (alpha in this case) that is tuned using the benchmark domains. In summary, I would have given this paper a higher rating if I had been convinced of either the real-world relevance of their positive theoretical result, or the generality of the GDPG algorithm. One minor comment is that the * subscript notation is a bit confusing, as * is typically used for the optimal value / policy.