Paper:
Sequence generation models are commonly refined with reinforcement learning over user-defined metrics. However, high gradient variance hinders the practical use of this method. To stabilize this method, we adapt to contextual generation of categorical sequences a policy gradient estimator, which evaluates a set of correlated Monte Carlo (MC) rollouts for variance control. Due to the correlation, the number of unique rollouts is random and adaptive to model uncertainty; those rollouts naturally become baselines for each other, and hence are combined to effectively reduce gradient variance. We also demonstrate the use of correlated MC rollouts for binary-tree softmax models which reduce the high generation cost in large vocabulary scenarios, by decomposing each categorical action into a sequence of binary actions. We evaluate our methods on both neural program synthesis and image captioning. The proposed methods yield lower gradient variance and consistent improvement over related baselines.

Review:
The paper presents a novel reinforcement learning-based algorithm for contextual sequence generation. The algorithm builds on the previously proposed MIXER algorithm and improves it by integrating gradient estimates with lower variance (augment-REINFORCE-swap-merge). To further improve the runtime complexity of the proposed algorithm, binary tree-based hierarchical softmax is applied. The algorithm is evaluated on the Karel dataset for neural program synthesis and the MS COCO dataset for image captioning.
The presentation of the paper must be improved (my score assumes that this will have been done). It is nice to have the detailed derivations when trying to dive deeper into the problem, but it hinders understanding of the main concepts at the first reading. Therefore, I would highly recommend to move most of the formulas to the appendix and keep instead only key ideas with intuitive explanations. It would also free some space in the main paper for the experiments from the appendix.
Several questions on the technical side:
1. Is there any intuition why pseudo actions tend to be equal to the true one when learning progresses? What causes this? Might it enforce any structure (like uniform)?
2. When all pseudo actions are the same, the gradient is zero. In theory, zero gradient of a function corresponds to its extremum. Does it mean that when all pseudo actions are the same, an extremum is reached or is it just an artifact of this particular estimator? Can one prove any results of this kind?
3. I understand that the ARSM estimator should be unbiased for V = 2. Does the estimator remain unbiased when V > 2?
4. In the experiments, the variance is shown to reduce significantly which is nice. However, in theory, does the ARMS guarantee non-increasing variance or can it potentially go up in some cases? If it can, have it ever been observed in practice?
5. How does the runtime of the proposed algorithm compare to the competitors?
Experiments:
1. Bunel et al (2018) report higher generalization on the Karel dataset. Is the difference due to the removal of the optional grammar checker? Can the same experiments be performed with this checker on or are there any constraints of the ARSM-based method?
2. The submitted code for the NPS experiment is actually the one by Bunel et al with their comments. I could not find any instructions or scripts reproducing the results of this paper (and I didn’t have much time to figure that out). One thing I wanted to check in the code is how the variance was computed for the plots?
Minor:
1. p. 4, “expected award” >> “expected reward”
2. g_{ARSM} defined twice in (5) and in the beginning of p. 4
3. “Fig. 1 (left two) plots” and “Fig. 1 (right two) plots” not good