I like the fact that the method is very simple to understand and implement (see my summary), and does not require any major changes to the base SG-MCMC algorithm. Also, this seems very general and applies to a large class of SG-MCMC algorithms, and is therefore potentially very impactful to the Stochastic Gradient MCMC community. Novelty: Although Richardson-Romberg extrapolation is well known in numerical analysis, it is not widely known in the machine learning / stochastic gradient MCMC community. Clarity: The paper is well written and the presentation is clear. Comments/questions: - Can this technique be directly applied to all SG-MCMC methods?

The paper describes a new method for FDR control for p-values with additional information. For each hypothesis, there is a p-value p_i, and there is also a feature vector X_i. The method learns the optimal threshold for each hypothesis, as a function of the features vector X_i. The idea seems interesting and novel, and overall the paper is explained quite clearly. In several simulated and real data example, the authors show that their method can use the additional information to increase the number of rejections, for a given FDR control threshold. It seems to me to be important that the X_i's were not used to calculate the P_i, otherwise we get a problem of circularity.

Non-parametric multivariate density estimation faces strong statistical and computational bottlenecks, and the more practical approaches impose near-parametric assumptions on the form of the density functions. In this paper, we leverage recent developments to propose a class of non-parametric models which have very attractive computational and statistical properties. Our approach relies on the simple function space assumption that the conditional distribution of each variable conditioned on the other variables has a non-parametric exponential family form.

The paper extends recent work of Scieur et al [2016] on nonlinear acceleration via extrapolation of sequences from deterministic to stochastic optimization. The work by Scieur itself generalizes and extends results developed in the late 60s and 70s from quadratics to non-quadratics (whence the name "nonlinear"). Sequence extrapolation methods seem to have been "forgotten" or simply "not in use" by the ML and optimization community until recently, and have some interesting theoretical and practical properties. For instance, nonlinear regularized acceleration (NRA) is capable to accelerate the sequence of iterates formed by the gradient descent method and obtain the optimal accelerated rate. This is done via what essentially amounts to a "bootstrapping" extrapolation process.

It has recently been shown that, when all the saddle points of a non-convex function are "strict saddle", then gradient descent with a (reasonable) random initialization converges to a local minimizer with probability one. For a randomly perturbed version of gradient descent, the convergence rate can additionally be shown to be polynomial in the parameters. This article proves that such a convergence rate does not hold for the non-perturbed version: there exists reasonably smooth functions with only strict saddle points, and natural initialization schemes such that gradient descent requires a number of steps that is exponential in the dimension to find a local minimum. I liked this article very much. It answers a very natural question: gradient descent is an extremely classical, and very simple algorithm.

This paper presents a formal condition for Byzantine fault-tolerant stochastic gradient aggregation, as well as an algorithm (Krum) that satisfies the condition. Given the definition, it is straightforward to see that aggregation based on linear combination (including averaging) is not Byzantine tolerant. Meanwhile the paper gives evidence that Krum is not only tolerant in theory but reasonably so in practice as well. I found the paper to be clear, well-organized, self-contained, and altogether fairly thorough. The basic motivation is clear: the literature on distributed learning has focused on statistical assumptions and well-behaved actors, but what can we do in very pessimistic conditions?

This paper proposes a LLoyd type method with PCA initialization to estimate means of Gaussians in a streaming setting. References seem to be severely lacking as the domain is wide. The key point of the algorithm seems to be the initialization and there is no discussion on this part (comparison with the literature on k-means initialization). While the technical results might be interesting I have difficulties commenting on them without the proper background on the subject. I find as well that the technical exposition of proofs is not very clear (notations, chaining of arguments).

Summary: This paper derives conditions for guaranteed improvement when using policy gradient methods. These conditions are for stochastic gradient estimates and also bound the amount of improvement with high probability. The authors then show how these bounds can be optimized by properly selecting the step size and batch size parameters. This is in contrast to previous work that only considers how the step size can be optimized. The result is an algorithm that can guarantee improvement with high probability.

Random projections are often used in learning tasks involving dimensionality reduction. The goal of the additional quantization step is data compression that allows for a reduction in space complexity of learning algorithms and more efficient communication in distributed settings.

This paper studies the problem of hierarchical clustering in a beyond-the-worst-case setting, where the data is a random graph generated by a Hierarchical Stochastic Block Model (HSBM). It proposes an SVD linkage algorithm and proves that in certain regimes it returns a solution that is a constant approximation to the cost function of hierarchical clustering proposed by Dasgupta. It also considers an algorithm that combines the SDP relaxation approach and recursive sparsest cut approach in previous works to get a constant approximation in larger regimes. Roughly speaking, the HSBM model considered assumes some underlying tree T* over k leaves (each leaf corresponding to a bottom cluster containing a certain number of vertices). Each node in the tree has some weight in (0,1) and a node's weight should not be larger than its descendant's.