Paper:
In many partially observable scenarios, Reinforcement Learning (RL) agents must rely on long-term memory in order to learn an optimal policy. We demonstrate that using techniques from natural language processing and supervised learning fails at RL tasks due to stochasticity from the environment and from exploration. Utilizing our insights on the limitations of traditional memory methods in RL, we propose AMRL, a class of models that can learn better policies with greater sample efficiency and are resilient to noisy inputs. Specifically, our models use a standard memory module to summarize short-term context, and then aggregate all prior states from the standard model without respect to order. We show that this provides advantages both in terms of gradient decay and signal-to-noise ratio over time. Evaluating in Minecraft and maze environments that test long-term memory, we find that our model improves average return by 19% over a baseline that has the same number of parameters and by 9% over a stronger baseline that has far more parameters.

Review:
# UPDATE after rebuttal
I have changed my score to 8 to reflect the clarifications in the new draft.
Summary:
This paper presents a family of architectural variants for the recurrent part of an RL controller. The primary claim is that simple components which compute elementwise sum/average/max over the activations seen over time are highly robust to noisy observations (as encountered with many RL environments), as detailed with various empirical and theoretical analyses. By themselves these aggregators are incapable of storing order dependent information, but by combining an LSTM with an aggregator, and pushing half the LSTM activations through the aggregator, and concatenating the the other half of the activations with the aggregator output, the resulting output contains order dependent and order independent content.
The motivation is very clear (many of the most challenging modern video games used as RL environments clearly have noisy observations, and many timesteps for which no new useful information is observed) and the related work is comprehensive. An increase in training speed and stability, apparently without any major caveats, would be of great interest to any practitioner of Deep Reinforcement Learning.
The experiments provided are good, and vary nicely between actual RL runs and theoretical analysis, all of which convinces me that this could well become a standard Deep RL component. I do have a range of questions & requests for clarification (see below) but I believe the experiments as presented, plus some additions before camera ready, will make for a good paper of wide interest.
Desicion: Accept. I would give this a 7 if I was able to. The idea is very simple (indeed I find it slightly hard to believe no one has tried this before, but I don't know of any references myself) and the results, particularly Figure 4, are compelling. It's nice to see a very approachable more mathematical analysis as well, it would be good to see more papers proposing new neural components with this kind of rigour. I look forward to trying this approach myself, post publication.
Discussion:
AMRL-Avg coming out the best in Figure 8 makes a lot of sense to me, as I can see how average provides a stable signal of unordered information. One thing that really doesn't make sense to me is why Max and Sum would also be good - obviously their SNR / Jacobians are quite similar, but fundamentally there is a risk of huge values being built up in activations (especially with Sum), which at least have the potential to cause numerical instability, provide weird gradient magnitudes (which then mess up moment tracking optimizers like Adam, etc). Thre does not seem to be any mention of numerical stability, or whether any considerations ned to be taken for this. Maybe we could hope that 'well behaved' internal neron activations are zero mean, so the average aggregator will never get too big - but is this always the case, at all points in training, in every episode? I appreciate the straight through estimator might ameliorate this, but it is not made entirely clear to me in the text that this is the reason for using it. Addressing this point would increase the strength of the argument.
Given that DNC was determined to be the strongest baseline in a few of the metrics, and that AMRL combines these aggregators with LSTM, an experiment that I'm surprised is missing would be to make AMRL containing a DNC instead of an LSTM. Is there a reason why this wasn't attempted?
It would have been good to see a wider set of RL experiments - the Atari suite is well studied, easily available, and there are many open source implementations to which AMRL could easily be slotted into (eg IMPALA, openai baselines, etc).
The action space for Minecraft is not spelled out clearly - at first I assumed this was the recent project Malmo release, which I assume to have continuous actions (or at least, the ability to move in directions that are not compass points), but while Malmo is mentioned in the paper, the appendix implies that the action space is (north, east, west) etc. I'm aware that there is precedent in the literature (Oh et al 2016) for 'gridworld minecraft', but I think it would improve the paper to at least acknowledge this in the main text, as I feel even most researchers in 2019 would read the text and assume the game to be analogous to VizDoom / DeepMind Lab, when it really isn't. Note that most likely the proposed method would give an even bigger boost with "real" minecraft, as there are even more non-informative observations between the interesting ones, and furthermore I think the environment choice made in this paper is fine, as it still demonstrates the point. A single additional sentence should suffice.
Minor points:
NTM / DNC were not "designed with RL in mind" per se, the original NTM paper had no RL and the DNC paper contained both supervised and RL results. Potentially the statement at the bottom of page 1 was supposed to refer mainly to stacked LSTMs - either way I feel it would be better to slightly soften the statement to "...but also for stacked LSTMs and DNCs (cite), which have been widely applied in RL."
In the RL problem definition, the observation function and the state transition function are stated as (presumably?) probability distributions with the range [0,1], but for continuous state / observation spaces it is entirely possible for the probability density at a point to exceed 1. 
Also in the RL section - the notation of $\tau_t \in \Omega^t$ should probably also contain the sequence of $t-1$ actions taken throughout the trajectory - this is made clear in the text, but not in the set notation.
The square bracket "slicing" notation used for slicing and concatenating is neat, but even though I spend all day writing python it still took me a while to realise what this meant, as I haven't seen this used in typeset maths before. Introducing this notation (as well as the pipe for concatenation) at first usage would help avoid tripping up readers unnecessarily.
Note that this pdf caused several office printers I tried it on to choke on later pages, and I get slow scrolling in Chrome on figures such as figure 11 - possibly the graphics are too high resolution (?)
typos: A5, feed forward section: "later" should be "layer" I believe.