Large mini-batch parallel SGD is commonly used for distributed training of deep networks. Approaches that use tightly-coupled exact distributed averaging based on AllReduce are sensitive to slow nodes and high-latency communication. In this work we show the applicability of Stochastic Gradient Push (SGP) for distributed training. SGP uses a gossip algorithm called PushSum for approximate distributed averaging, allowing for much more loosely coupled communications, which can be beneficial in high-latency or high-variability scenarios. The tradeoff is that approximate distributed averaging injects additional noise in the gradient which can affect the train and test accuracies. We prove that SGP converges to a stationary point of smooth, non-convex objective functions. Furthermore, we validate empirically the potential of SGP. For example, using 32 nodes with 8 GPUs per node to train ResNet-50 on ImageNet, where nodes communicate over 10Gbps Ethernet, SGP completes 90 epochs in around 1.6 hours while AllReduce SGD takes over 5 hours, and the top-1 validation accuracy of SGP remains within 1.2% of that obtained using AllReduce SGD.

Gradient descent is an optimisation method for finding the minimum of a function. It is commonly used in deep learning models to update the weights of the neural network through backpropagation. In this post, I will summarise the common gradient descent optimisation algorithms that are used in popular deep learning frameworks (e.g. The purpose of this post is to make it easy to read and digest since there aren't many of such summaries out there, and as a cheat sheet if you want to implement them from scratch. I have implemented SGD, momentum, Nesterov, RMSprop and Adam in a linear regression problem using gradient descent demo here using JavaScript.

Coded computation techniques provide robustness against straggling servers in distributed computing, with the following limitations: First, they increase decoding complexity. Second, they ignore computations carried out by straggling servers; and they are typically designed to recover the full gradient, and thus, cannot provide a balance between the accuracy of the gradient and per-iteration completion time. Here we introduce a hybrid approach, called coded partial gradient computation (CPGC), that benefits from the advantages of both coded and uncoded computation schemes, and reduces both the computation time and decoding complexity.

Scalable Bayesian sampling is playing an important role in modern machine learning, especially in the fast-developed unsupervised-(deep)-learning models. While tremendous progresses have been achieved via scalable Bayesian sampling such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD), the generated samples are typically highly correlated. Moreover, their sample-generation processes are often criticized to be inefficient. In this paper, we propose a novel self-adversarial learning framework that automatically learns a conditional generator to mimic the behavior of a Markov kernel (transition kernel). High-quality samples can be efficiently generated by direct forward passes though a learned generator. Most importantly, the learning process adopts a self-learning paradigm, requiring no information on existing Markov kernels, e.g., knowledge of how to draw samples from them. Specifically, our framework learns to use current samples, either from the generator or pre-provided training data, to update the generator such that the generated samples progressively approach a target distribution, thus it is called self-learning. Experiments on both synthetic and real datasets verify advantages of our framework, outperforming related methods in terms of both sampling efficiency and sample quality.

We consider the structured-output prediction problem through probabilistic approaches and generalize the "perturb-and-MAP" framework to more challenging weighted Hamming losses, which are crucial in applications. While in principle our approach is a straightforward marginalization, it requires solving many related MAP inference problems. We show that for log-supermodular pairwise models these operations can be performed efficiently using the machinery of dynamic graph cuts. We also propose to use double stochastic gradient descent, both on the data and on the perturbations, for efficient learning. Our framework can naturally take weak supervision (e.g., partial labels) into account. We conduct a set of experiments on medium-scale character recognition and image segmentation, showing the benefits of our algorithms.

The success of deep networks in a range of prediction tasks has raised the question of whether they can serve as models for processing in the cortex [4, 8]. These networks are most successful when trained using versions of stochastic gradient descent, where small random subsets of training data are used to compute the gradient of the loss function with respect to the weights connecting subsequent layers and then update them. Due to the particular structure of the function represented by these multi-layer networks the 1 gradient is computed using back-propagation - an algorithmic formulation of the chain rule. In all but the last layer, the gradient of a weight in this algorithm is a product of the activity of the units it connects - the pre-synaptic input unit in the lower layer and the post-synaptic output unit in the higher layer. In that sense it is performing a form of local Hebbian learning: the update depends on the product of the feedback activity in the post-synaptic unit (the error signal) and the activity of the pre-synaptic unit.

Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein gradient flows. With a rigorous non-asymptotic convergence theory developed recently, SPOS avoids the particle-collapsing pitfall of SVGD. Nevertheless, variance reduction in SPOS has never been studied. In this paper, we bridge the gap by presenting several variance-reduction techniques for SPOS. Specifically, we propose three variants of variance-reduced SPOS, called SAGA particle-optimization sampling (SAGA-POS), SVRG particle-optimization sampling (SVRG-POS) and a variant of SVRG-POS which avoids full gradient computations, denoted as SVRG-POS$^+$. Importantly, we provide non-asymptotic convergence guarantees for these algorithms in terms of 2-Wasserstein metric and analyze their complexities. Remarkably, the results show our algorithms yield better convergence rates than existing variance-reduced variants of stochastic Langevin dynamics, even though more space is required to store the particles in training. Our theory well aligns with experimental results on both synthetic and real datasets.

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD) reinforcement learning methods can be formally derived, not by starting from their original objective functions, as previously attempted, but rather from a primal-dual saddle-point objective function. We also conduct a saddle-point error analysis to obtain finite-sample bounds on their performance. Previous analyses of this class of algorithms use stochastic approximation techniques to prove asymptotic convergence, and do not provide any finite-sample analysis. We also propose an accelerated algorithm, called GTD2-MP, that uses proximal "mirror maps" to yield an improved convergence rate. The results of our theoretical analysis imply that the GTD family of algorithms are comparable and may indeed be preferred over existing least squares TD methods for off-policy learning, due to their linear complexity. We provide experimental results showing the improved performance of our accelerated gradient TD methods.

A key factor in developing high performing machine learning models is the availability of sufficiently large datasets. This work is motivated by applications arising in Software as a Service (SaaS) companies where there exist numerous similar yet disjoint datasets from multiple client companies. To overcome the challenges of insufficient data without explicitly aggregating the clients' datasets due to privacy concerns, one solution is to collect more data for each individual client, another is to privately aggregate information from models trained on each client's data. In this work, two approaches for private model aggregation are proposed that enable the transfer of knowledge from existing models trained on other companies' datasets to a new company with limited labeled data while protecting each client company's underlying individual sensitive information. The two proposed approaches are based on state-of-the-art private learning algorithms: Differentially Private Permutation-based Stochastic Gradient Descent and Approximate Minima Perturbation. We empirically show that by leveraging differentially private techniques, we can enable private model aggregation and augment data utility while providing provable mathematical guarantees on privacy. The proposed methods thus provide significant business value for SaaS companies and their clients, specifically as a solution for the cold-start problem.

University of Wisconsin-Madison Abstract Neural networks have great success in many machine learning applications, but the fundamental learning theory behind them remains largely unsolved. Learning neural networks is NPhard, but in practice, simple algorithms like stochastic gradient descent(SGD) often produce good solutions. Moreover, it is observed that overparameterization-- designing networks whose number of parameters is larger than statistically needed to perfectly fit the data -- improves both optimization and generalization, appearing to contradict traditional learning theory. In this work, we extend the theoretical understanding of two and three-layer neural networks in the overparameterized regime. We prove that, using overparameterized neural networks, one can (improperly) learn some notable hypothesis classes, including two and three-layer neural networks with fewer parameters. Moreover, the learning process can be simply done by SGD or its variants in polynomial time using polynomially many samples. We also show that for a fixed sample size, the generalization error of the solution found by some SGD variant can be made almost independent of the number of parameters in the overparameterized network. Authors sorted in alphabetical order. 1 Introduction In contrast to the widely accepted empirical success, much less theory is known. Despite a recent increase of theoretical studies, many questions remain largely open, including fundamental ones about the optimization and generalization in learning neural networks.