__ Summary and Contributions__: This paper introduces an extension to SAC/TD3 type actor-critic algorithms. It models the critic with a generator network (actually twin delayed networks) and models the stochastic actor as a diagonal gaussian which also receives a noise input. The paper includes derivations required for approximating the entropy of their semi-implicit actor along with experiments showcasing improved performance on a standard sweet of deep RL control problems.

__ Strengths__: This work provides a good balance between analytical and empirical results. The method appears to be sound and does introduce a novel component--the semi-implicit actor and associated entropy estimation. The empirical results show a clear trend of improved performance over previous algorithms on an appropriate suite of RL tasks. And their ablation experiments are helpful at establishing the importance of each component of their overall algorithm.

__ Weaknesses__: One possible weakness of this work is the somewhat incremental nature of the improvement. For example one of the stated contributions is to apply the twin-delayed technique to learning the critic, which is well established.

__ Correctness__: Yes, the algorithm and derivation of loss functions appear correct, and then empirical methodology appears to compare the new algorithm against baseline techniques on a fair basis, with any possible confounding factors removed.
Since the Ant-v2 environment is one in which the TD3 baseline outperforms the proposed method, it would be interesting to include ablation studies on this environment, as well. And likewise with Humanoid, since it has such a large performance gap between SAC and TD3.
The authors claim that the semi-implicit actor can represent more complicated policy distributions, include skewness, etc., even through the diagonal-gaussian parameterization, and that this capability is useful for learning more complicated tasks. This claim is straightforwardly appealing, and is supported by their ablation experiments (Fig 3) and the visualization of the policy (Fig 2b). However the claim could be made much more strongly, for example by tying the distribution in Fig 2b to a particular behavior pattern which was not possible with the diagonal gaussian alone, or by showing an example like in Fig 2b but from later in training. As written, Fig 2b is from early in training, which could mean its very non-diagonal shape is more a result of random initialization than of learning?

__ Clarity__: The paper is mostly well organized and written. Overall I would encourage some minor revisions for clarity in due course.

__ Relation to Prior Work__: Most of the discussion on prior work is satisfactory, however there appears to be a lot of overlap between the methods/developments in this paper and in the paper cited for the algorithm SDPG. It would be helpful to draw more explicit parallels/distinctions from that work, otherwise it appears at first glance to make the current work more incremental. Overall the related work section could be expanded slightly to discuss more explicitly the implications from prior work on the current paper, slightly beyond the brief statements of existence currently included.

__ Reproducibility__: Yes

__ Additional Feedback__:

__ Summary and Contributions__: The paper considers the model-free Reinforcement Learning setting with continuous actions, and proposes a new algorithm that increases sample-efficiency. The proposed algorithm consists of two elements: a novel critic, built on ideas from the Distributional RL literature, but adapted to continuous actions, and a novel actor, that combines an explicit component (a Gaussian-based function) and an implicit component (one of the inputs of the Gaussian is a randomly-sampled epsilon, as in Generative Networks). The resulting algorithm is empirically shown to lead to state-of-the-art results.

__ Strengths__: The paper is extremely well-written, clear and compact. The amount of equations in the paper illustrates how much information has to be compactly conveyed by the paper, yet everything is easy to follow (for an expert in discrete-action RL, but not continuous actions).
The proposed algorithm is quite complicated, and has many original components to it, but every component is clearly motivated (the distributional aspect is motivated, as is why two critics and a minimum are used, or why a semi-implicit actor is necessary). The empirical evaluation is convincing, and the authors take care to evaluate the fairness of their evaluation, in their case by ensuring that all the algorithms are built on the same code-base.
The results presented in the paper are highly significant, and the algorithm itself makes few assumptions (not more than PPO or other continuous-action algorithms). As such, it can be applied to a wide variety of problems. An added bonus is that the code of the proposed algorithm is available in the supplementary material, which ensures that a baseline exists, and that the paper can be reproduced.

__ Weaknesses__: The compactness of the papers led me to miss the exact definition of the sorting operation happening in the critic (the authors addressed that concern by clarifying their notations in the author response, I suggest that they put that clarification in the paper). For reference, my remark was as follows: the critic algorithm is built around a sorting operation, that is not fully described on two levels. First, it is unclear whether the sorting function is applied to a single vector of floating-point values, and sorts them (as Equation 4 would indicate, with arrows put above vectors), or whether vectors in a batch of vectors are being sorted (as relatively explicitly shown between Equations 8 and 9). In the second case, how vectors are sorted should have been defined, as it is unclear how they are compared (are their norms being compared, or is a hierarchical comparison between their components being performed?).
The presence of source code allows an answer for this question to be found relatively easily, but the absence of that little practical details makes imagining the algorithm as the paper is read more difficult.

__ Correctness__: The theoretical contributions in the paper flow well, and do not raise questions about correctness. The empirical evaluation is thorough, fair, and uses modern, high-performance algorithms as baselines.

__ Clarity__: The paper is well-written and easy to understand, even for someone familiar with most of the concepts presented in the paper (distributional RL, GAN networks, the Soft Actor-Critic), but not expert in these particular domains. Someone less familiar with the work the paper builds on may have a harder time following the paper, as it remains quite dry, but I don't see how the paper could be made easier on the reader without exceeding the page limit.

__ Relation to Prior Work__: The paper thoroughly discusses related work and emphasizes its contributions in a satisfactory way. There are some cases, such as Equation 5, where it is a bit more difficult to see if the contribution of the paper is the use of an existing equation in a new setting, or a new equation. Sentences such as "Inspired from [X], we propose to use something that looks a bite like [Y]" often lead to confusion, as they indicate that the equation that will follow will not be X, but the sentence does not indicate whether Y contains X (and so, the following equation is Y in a new context), or if Y did not know about X, and the following equation is an original combination of X and Y.

__ Reproducibility__: Yes

__ Additional Feedback__: There was a discussion among the reviewers about the novelty of this paper, and its relation with other work on distributional RL and generative methods. The novelty of this paper became clear after very attentive reading. I therefore suggest that the novel components of the actor and critic presented in this paper are better emphasized in the introduction of the paper, and compared to other work.

__ Summary and Contributions__: This paper proposes a new algorithm (implicit distributional actor critic; IDAC) which uses a distributional critic and a richer representation of the actor policy (semi-implicit actor; SIA). The implicit distributional critic uses twin delayed deep generator networks to limit over-estimation problems, and the implicit policy is argued to provide improved exploration. Performance is evaluated, in comparison with SAC/TD3/PPO, on several Mujoco continuous control environments.

__ Strengths__: I would consider the structure of the empirical work to be one of the highlights of the paper. Besides the generally positive results, the authors do a good job of proposing clear experimental questions and systematically evaluating them. The ablation study in particular helps to support the proposed setup in this work.

__ Weaknesses__: Except for in ablation, the proposed method is not sufficiently compared against other similar approaches. That is, while it is compared with other RL algorithms, the only other method compared with that is using similar approaches for the critic or actor (both of which have closely related work) was an extremely recent unpublished work on SDPG, and this was only shown in the ablation study (as opposed to over the larger set of environments in Figure 1). My concern here is that while this paper shows that a distributional critic and implicit policy improve performance, it is not entirely clear that the proposed form of these is any better than those already proposed in prior work. Again, with the caveat that they do compare with a method from a very recent paper that has not been published, as well as that the ablation does (to a limited degree) cover some variations in the approach.

__ Correctness__: One of the claims in the contributions was that the flexibility of SIA would improve exploration. This does not seem to have been evaluated, and while I share the author’s intuition on this, it is something that should be phrased as a hypothesis rather than a contribution.
Section 2.2 seems to want a formal result showing that this approach to learning the distribution of returns is principled. As there is no consistent connection between \epsilon^{(k)} and \tau_i, I do not see why the proposed method is necessarily better than simply minimizing the sample Wasserstein, which as noted can produce biased gradients.

__ Clarity__: I thought this paper was reasonably clear and well written.

__ Relation to Prior Work__: Overall, I like the direction of the work, and agree with the authors point about the implicit parameterization of the actor potentially leading to better exploration. I think this would be a great contribution if it was properly investigated. I have some minor concerns about the convergence properties of the proposed distributional critic. Finally, my biggest issue is with regards to related work. There’s a good chance that the choices made in this paper are actually superior to those made in the paper I mentioned, but this work would need to have significant chances to allow a clear comparison with it.
Pseudo-code in the appendix *really* stretches the boundary between mathematical definition and pseudo-code. Providing actual pseudo-code would be preferable.
L128: “In the same sprite” perhaps should be “spirit”?

__ Reproducibility__: Yes

__ Additional Feedback__: Overall, I like the direction of the work, and agree with the authors point about the implicit parameterization of the actor potentially leading to better exploration. I think this would be a great contribution if it was properly investigated. I have some minor concerns about the convergence properties of the proposed distributional critic. Finally, my biggest issue is with regards to related work. There’s a good chance that the choices made in this paper are actually superior to those made in the paper I mentioned, but this work would need to have significant chances to allow a clear comparison with it.
Pseudo-code in the appendix *really* stretches the boundary between mathematical definition and pseudo-code. Providing actual pseudo-code would be preferable.
L128: “In the same sprite” perhaps should be “spirit”?
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Update:
After reading the rebuttal and discussing with other reviewers, I believe the author's have addressed my main concerns and have updated my score. I would emphasize the author(s) discussion of the differences with DPO should be included in the final version in some form.

__ Summary and Contributions__: This paper proposes to use more flexible parameterizations for distributional Q-learning and for continuous-action policies, aiming to better model the maximum-entropy policy distribution in a soft actor critic-like setting. It introduces (1) an implicit distributional value function, which produces a sampled value estimate given a state, action, and a noise vector; (2) a semi-implicit policy parameterization, which can represent richer distributions than the typical Gaussian policy; and (3) tractable learning algorithms for both value function and policy.
The paper includes thorough experimental results on standard benchmarks, as well as ablations to attempt to show the contribution of each component of the method.
**Post rebuttal**
Thanks to the authors for your response, which cleared things up for me. I stand by my original score and think this would be a solid paper for NeurIPS.

__ Strengths__: This work introduces a semi-parametric policy class which is interesting and seems to be able to capture more complex multi-modal structure. It provides evidence that richer policy parameterizations can lead to improved performance, although as has been observed in the past with mixture-of-Gaussians or normalizing flows policies this gain is typically small. The multimodal structure of the learned policy is verified empirically.
The ideas introduced around training the implicit distributional value function are new to me, as is the elementwise minimization over the sampled values.
The ablation study is thorough and may be of use to others in the community who are attempting to make decisions about which methods to use, e.g. implicit policy versus Gaussian policy or single critic versus twin-delayed critic.

__ Weaknesses__: Some decisions in the paper are not well motivated, and despite the extensive set of ablations the importance of some choices remains unclear.
There are really two separate methodological improvements proposed in this paper: the implicit distributional value function and the semi-implicit policy. These two components might have been better off proposed separately so that they could be studied in more detail. One paper could propose the implicit parameterization of the distributional value function and compare its results to C51 and QR-DQN, while another used a standard expected-value critic with the semi-implicit policy and evaluated in detail the impact of the policy parameterization compared to Gaussian, mixture of Gaussian, and normalizing flow policies.
Further complicating matters, there are a lot of bells and whistles in the final method (twin delayed critics, learned temperature, etc). While ablations help a lot, all the tricks do muddle my understanding of which improvements are contributing what.
I do not understand clearly the motivation behind using an implicit distribution for the value function. With a 1D function, especially given that the loss being used is based on quantiles anyway, what is to be gained by using an implicit distribution instead of quantile regression?

__ Correctness__: I'm probably missing something, but where did the normalizing integral for G go between equations 13 and 14?
Should the $\pi_\theta(a^{(1)} | s, \xi^{(\ell)})$ have $a^{(\ell)}$ instead?
As I understand it the SAC results are using the original version of SAC [16] rather than the modern version [41] with the learned temperature — please clarify if this is incorrect. Given that this method uses the learned temperature parameter from [41], it should compare against that version of SAC.

__ Clarity__: Overall the paper is acceptably well-written, but it could be clearer. Due to having two largely independent contributions in the same paper, things can get a bit muddled at times.
In the caption for Table 1, what is meant by "average maximal returns"? What is being maximized over?

__ Relation to Prior Work__: Yes

__ Reproducibility__: Yes

__ Additional Feedback__: It would really help the work to very precisely state in the introduction what the problem is that you're trying to solve, the method you're proposing, and why this method solves it. For example, the paragraph starting at line 50 argues for the SIA by saying that it will fully take advantage of the distributional return modeled by the DGN. This has two problems:
1. It is not true. The noise in the DGN is averaged out in the policy update such that the new policy is based only on the expected value of each action (Equation 13).
2. It does not connect back all the way to the end objective of the paper. If the goal of the method is to have faster policy learning due to better exploration, argue for that, and motivate why you think this is the right way to do it.
Right now the motivation for the paper reads like you simply wanted to combine a few things; it would be much stronger to say precisely why.