Recent works have shown that line search methods can speed up Stochastic Gradient Descent (SGD) and Adam in modern over-parameterized settings. However, existing line searches may take steps that are smaller than necessary since they require a monotone decrease of the (mini-)batch objective function.

Variance reduction has emerged in recent years as a strong competitor to stochastic gradient descent in non-convex problems, providing the first algorithms to improve upon the converge rate of stochastic gradient descent for finding first-order critical points. However, variance reduction techniques typically require carefully tuned learning rates and willingness to use excessively large "mega-batches" in order to achieve their improved results.

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Langevin dynamics (MFLD) (Mei et al., 2018; Hu et al., 2019) is particularly attractive due to the MFLD arises from a noisy gradient descent update on the parameters, where Gaussian noise is injected to the gradient to encourage "exploration". Furthermore, uniform-in-time estimates of the particle discretization error have also been established (Suzuki et al., The goal of this work is to address the following question.

We apply the derived computational error bounds to study the generalization performance ofmulti-pass stochastic gradient descent (SGD) ina non-parametric setting.

In this work, we showthat this "lazy training" phenomenon isnot specific tooverparameterized neural networks, and is due to a choice of scaling, often implicit, that makes the model behave as its linearization around the initialization, thus yielding amodel equivalenttolearning withpositive-definite kernels.

Unfortunately, computing the gradient of a spectral function is generally of cubic complexity, as such gradient descent methods are rather expensive for optimizing objectives involving the spectral function.

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We introduce Bayesian distributed stochastic gradient descent (BDSGD), a high-throughput algorithm for training deep neural networks on parallel computing clusters. This algorithm uses amortized inference in a deep generative model to perform joint posterior predictive inference of mini-batch gradient computation times in a compute cluster specific manner. Specifically, our algorithm mitigates the straggler effect in synchronous, gradient-based optimization by choosing an optimal cutoff beyond which mini-batch gradient messages from slow workers are ignored. The principle novel contribution and finding of this work goes beyond this by demonstrating that using the predicted run-times from a generative model of cluster worker performance improves over the static-cutoff prior art, leading to higher gradient computation throughput on large compute clusters. In our experiments we show that eagerly discarding the mini-batch gradient computations of stragglers not only increases throughput but sometimes also increases the overall rate of convergence as a function of wall-clock time by virtue of eliminating idleness.