Paper:
We study the use of hypermodels to represent epistemic uncertainty and guide exploration. This generalizes and extends the use of ensembles to approximate Thompson sampling. The computational cost of training an ensemble grows with its size, and as such, prior work has typically been limited to ensembles with tens of elements. We show that alternative hypermodels can enjoy dramatic efficiency gains, enabling behavior that would otherwise require hundreds or thousands of elements, and even succeed in situations where ensemble methods fail to learn regardless of size. This allows more accurate approximation of Thompson sampling as well as use of more sophisticated exploration schemes. In particular, we consider an approximate form of information-directed sampling and demonstrate performance gains relative to Thompson sampling. As alternatives to ensembles, we consider linear and neural network hypermodels, also known as hypernetworks. We prove that, with neural network base models, a linear hypermodel can represent essentially any distribution over functions, and as such, hypernetworks are no more expressive.

Review:
The authors demonstrate advantages of a linear hypermodel over an ensemble method in exploration guided by epistemic uncertainty. They perform an empirical study in the bandit setting and claim that their approach both outperforms the ensemble method and offers a significant increase in computational efficiency. The theoretical contribution is that they prove universality in the sense that an arbitrary distribution over functions can be represented by a linear hypermodel. The experiments support their claims. Some of the explanations, however, are confusing, and relations to prior work should be clarified. 
Figure 3 shows a surprisingly large performance gap between the hypermodel and the ensemble method as the number of actions increases. But how about comparing linear hypermodels with different index sizes? Do we also expect asymptotic improvement as we increase the index size?
Imprecise or confusing explanations in the paper:
1) Page 2, first Q: In theory, the effectiveness of the ensemble method should converge to that of the hypermodel as the ensemble size increases. They only tried ensemble size [10, 30, 100, 300] and then concluded that linear hypermodel can be effective regardless of the size of ensembles. Why?
3) Page 3, Section 2.1, second paragraph, first sentence: Please clarify a bit more what do you mean by perturbing data? Random shuffling of the dataset in each training epoch? What does ‘response variables’ mean?
4) Page 3, Section 2.1, second paragraph, last 2 sentences about $A_t$: we guess it should be $A_t ~ N(0, I)$ if $p_z$ is unit Gaussian according to the description in this paragraph. The current text claims it is the other way around, perhaps a typo?
5) Page 3, Section 2.1, first equation: Why take the inner product between $a$ and $z$ ? How does this reflect the randomized computation (the motivation for augmented random vector $A_t$)? The objective is to maximize the log-likelihood of the prediction under the Gaussian assumption. Please clarify the assumptions about random variables $Y_t$ at the beginning of this paragraph. 
6) Same place as in 5): Why regularize hypermodel parameters such that they are not too far from the initial vector? Is $\nu_0$ actually the additive prior model described in Section 2.5?
7) Page 3, Section 2.1, second equation: why multiply $|D|$ in the first term within the parentheses? Why not just $1/|D_tilde|$ to average the prediction error over the mini-batch?
8) Page 3, Section 2.1, second equation: is the cardinality of the index set $|Z_tilde|$ independent of mini-batch size? I.e. for each training data point there could be multiple models realized by multiple indices $z$
9) Page 4, Section 2.5: Why use this decomposition for training the hypermodel? If the intuition is to keep the initial weight small, what if we just simply initialize small values for $f_\theta(x)$ without decomposition?
10) Page 5, last second sentence: The notation of partition (the set notation after ‘Here,….’) is supposed to be $\hat{\mathcal{Z}}_{x^*} = \{ z\in \hat{\mathcal{Z}} | x^* in \argmax_{x} f_{g_{\nu}(z)}(x) \}$
Minor typos:
- Page 2, third paragraph: ‘…we compare their [efficacy] when used...’ ->  [efficiency] ?
- Page 2, the last paragraph before Section 2, first sentence: ‘Approaches to approximating TS and [informatino]-directed sampling...’ -> [information]
Relations to prior work:
1. Page 2: Hypernetworks (where one neural net learns to generate the weights of another net) are much older than this recent reference of 2016. One should relate this work to the original references since 1991 [FAST0-3a][FAST5][FASTMETA1-3][CO2] in section 8 of the overview http://people.idsia.ch/~juergen/deep-learning-miraculous-year-1990-1991.html 
2. Intro 2nd par: dropout was first published much earlier in 1990 as the stochastic delta rule: 
Hanson, S. J.(1990). A Stochastic Version of the Delta Rule, PHYSICA D,42, 265-272. See also arXiv:1808.03578, 2018. 
We might improve our rating provided the comments above were addressed in a satisfactory way in the rebuttal.
Edit after rebuttal: The authors replied: "Thanks for pointing out typos and citations that we will add." But apparently in the revised PDF this did not happen.