We examine the use of different randomisation policies for stochastic gradient algorithms used in sampling, based on first-order (or overdamped) Langevin dynamics, the most popular of which is known as Stochastic Gradient Langevin Dynamics. Conventionally, this algorithm is combined with a specific stochastic gradient strategy, called Robbins-Monro. In this work, we study an alternative strategy, Random Reshuffling, and show convincingly that it leads to improved performance via: a) a proof of reduced bias in the Wasserstein metric for strongly convex, gradient Lipschitz potentials; b) an analytical demonstration of reduced bias for a Gaussian model problem; and c) an empirical demonstration of reduced bias in numerical experiments for some logistic regression problems. This is especially important since Random Reshuffling is typically more efficient due to memory access and cache reasons. Such acceleration for the Random Reshuffling policy is familiar from the optimisation literature on stochastic gradient descent.

Update: The authors have helpfully pointed out that they do provide some guidelines on setting the hyperparameters. This paper creatively combines underdamped Langevin MCMC work of Cheng et al. with the gradient estimator SPIDER of Fang et al. This allows the paper to use the theoretical result from Fang et al. to prove a better bound for achieving epsilon in 2-Wasserstein distance. Effectively it is the UL-MCMC algorithm with a better gradient estimator. This isn't meant to imply that the work is trivial as adapting any insight from the optimisation literature for use in a HMC algorithm requires careful work to yield measurable improvements.

The reviewers expressed concern on the novelty of the algorithm, but still think it is well written and should be accepted for NIPS. We encourage the authors to carefully revise the work for the final version.

A key quantity in the analysis is p_j, the probability of missing j-th feature. Is this quantity given in advanced? Under MCAR, it can be easily estimated. But some clarifications are needed. Essentially, this method is just SGD IPW (though it is coordinate-wise IPW not the regular IPW).

The paper addresses the issue of missing values in SGD. There was agreement that the obtained results are novel but there was no strong advocate for the paper.

Originality: For the aforementioned contributions, I believe this work provides a creative, unique approach to this problem. Quality: I believe this paper to be technically sound, a complete work that presents interesting approaches for hierarchical clustering. Clarity: The paper is written well and clearly explains the approach. But there were a some details that I thought could have been made clearer in both the presentation and in the experiments. Unless I've missed something, I think that it would be good to more clearly state the process (and its complexity) of going from the ultrametric fit to data to a dendrogram.

The authors develop a nice method for fitting a hierarchical clustering by solving an optimization problem that leads to an ultrametric (and thus a hierarchical clustering). The reviewers are in agreement that this work should be accepted.

I agree with R3 that you did a poor job on relating your work to existing methods, in particular SARAH. Please also make sure that you carefully address the question of optimality. I also realized that your method in fact has nothing to do with momentum. Consider for instance deterministic objective, f(x, \xi) f(x). If one has a tight estimate, i.e. d_{t-1} abla f(x_{t-1}), then from your update rules it follows that d_t abla f(x_t), i.e. the method become gradient descent with no momentum! Your title, thus, is very confusing and I highly encourage you to change it.

This paper considers a communication efficient distributed optimization algorithm based on ADMM for stochastic optimization. The main idea is to perform multiple steps (can be timevarying) of stochastic gradient updates before the agents communicate, and therefore improving the communication efficiency. The proposed algorithm is shown to converge (in objective value & constraint violation) under a general non-smooth, non-strongly convex settings with O(1/eps) communication rounds and O(1/eps 2) unbiased gradient oracle calls. Other setting such as smooth strongly convex and non-smooth strongly convex are also analyzed and presented. Using multiple steps is however not novel.

After response----I keep my evaluation on the technical innovation and suboptimality of this paper. The basic Spider and SpiderBoost algorithms are both for first-order stationary point, they are almost the same, and both give n {1/2} rate. The simple way to modify both algorithms to escape saddle point is to add Negative Curvature Search (NCS) subroutine (which can be done in a very modular way, and is already shown in the Spider paper). I'd say it's almost trivial to also show SpiderBoost NCS to find second-order stationary point with n {1/2} rate. Comparing this paper with SpiderBoost NCS, there's no improvement from n {2/3} to n {1/2} (since Spiderboost is already n {1/2}), no simplification of Spider (as Spiderboost already did so). The only difference is replacing NCS by perturbations, which again requires some work, but most techniques are already there.