The paper has claimed three contributions, answering three questions. In general, I think removing boundedness assumption is useful. But Reviewer 3 pointed out that this work adds the "bounded level set" assumption and bounded gradient assumption, which do not seem much stronger than "bounded iterates". In particular, the gap between "bounded level-set" and "bounded iterates" is quite technical (not necessarily small, but not necessarily large), thus requires more explanation. R1 clarified that he was not claiming "[17, 18] or Pemantle alone already covered this paper's result", but asking whether a simple combination of [17, 18] and Pemantle [27] would give their result (that's why R1 used "morally" in the review).

Summary and Contributions: The paper proposes a model selection algorithm called Model Selection with Automated Online Experiments (AOE) that is designed for use in production systems. In the problem statement, it is stated that the goal of the model selection problem is to select the model from a set of candidate models that maximises a metric of interest. It is assumed that the metric of interest can be expressed as the average immediate feedback from each of a model's predictions. AOE uses both historical log data and data collected from a small budget of online experiments to inform the choice of model. A distribution for the accumulative metric, or expected immediate feedback, is derived.

This paper proposes an extension to Bayesian optimization methods for model selection. A surrogate model for the dataset is added to the setup, which allows the optimization to take more information to account as data is collected over time. The reviewers generally thought this was an interesting approach and an important direction. The main debate focused on the significance of the synthetic results based on real data, and whether they can be expected to generalize. We think that the clear novelty and the positive results outweigh this weakness.

Weaknesses: The constants in the bounds depend linearly on the dimension, although they depends exponentially on the regularization parameter. If Sinkhorn distance is thought as a proxy of the Wasserstein distance, this seems to be a hidden dependance on the dimension, since the regularization parameter plays the role of an interpolation between MMD and Wasserstein distances, and MMD distances are more blind to the dimension. This is not discussed in the paper. The results also have an exponential dependence on an assumed uniform upper bound on the cost. For the classical quadratic cost, this imply an exponential dependence on the dimension for the case of measures supported on [0,1] d for instance.

This paper proposes a new method to compute the (Sinkhorn) of barycenter of several probability measures. In practice, the method scales well computationally and in high-dimension and the authors provide some theoretical support. Reviewers agree that this paper is strong with only minor weaknesses (such as the exponential dependency in 1/gamma; which in related work is often suboptimal). I thus recommend accept (poster).

Summary and Contributions: The paper considers a graph clustering on directed graphs. The authors introduce a new notion of clustering objective denoted by flow ratio. For any ordered partition of vertex set V into k pairwise disjoint subset (S0, ..., Sk-1), the flow ratio of the partition is sum of the average flow (i.e. The optimal clustering is the partitioning of V that maximizes the flow ratio among all possible partitions. The authors represent the directed graph using the Hermitian adjacency matrix.

This paper considers the off-policy learning problem for the case of continuous treatments, and provides regret bounds for the doubly-robust estimator, as well as study of semiparametric efficiency. The primary assumptions are that the "value function" is of known parametric form in the treatment, but with arbitrary dependence on covariates. The proposed approach for continuous treatments avoids the unfavorable dimension dependence of previous approaches for continuous treatments, instead the difficulty is in the matrix regression problem of the covariance-based generalization of the propensity score for the continuous case. Quality: The paper is technically sound with claims well supported by theoretical analysis. Clarity: The paper is overall clear but sometimes vague in descriptions.

All the reviewers enjoyed your paper and recommended acceptance. Please try to ensure that the clarifications promised in the rebuttal make their way into the camera ready.

This work provides a detailed Renyi DP analysis of a modified MCMC acceptance test, and empirically demonstrates its efficacy. Originality: the RDP analysis and modified acceptance test is a novel contribution. Quality: the work is a complete piece on exploring this MCMC method, with a detailed analysis and experiments. Clarity: the work is fairly clearly written, but it can be easy to lose track of exactly what parameters remain as choices to be tuned in a list of various corrective factors and approximations. Significance: the work gives an MCMC method with privacy without convergence, which permits privacy guarantees to be given over a multitude of problems without doubts or guess work about when to stop the chain.

Although the analysis follows some known ideas from the literature on private SGD, there are a number of new tricks which make the current approach interesting, most notably the observation that one can use randomized acceptance tests to preserve privacy in an MCMC algorithm. When preparing the final version of this manuscript the authors should carefully consider the points raised in the reviews regarding: clarifying where the contributions lie with respect to previous work; provide high-level intuitions of the proofs to help a reader navigate the derivations; discuss the role of approximations used in the paper, where they affect the privacy or utility of the method, and where there is some room left for improvement.