Dieuleveut, Aymeric


Communication trade-offs for synchronized distributed SGD with large step size

arXiv.org Machine Learning

Synchronous mini-batch SGD is state-of-the-art for large-scale distributed machine learning. However, in practice, its convergence is bottlenecked by slow communication rounds between worker nodes. A natural solution to reduce communication is to use the \emph{`local-SGD'} model in which the workers train their model independently and synchronize every once in a while. This algorithm improves the computation-communication trade-off but its convergence is not understood very well. We propose a non-asymptotic error analysis, which enables comparison to \emph{one-shot averaging} i.e., a single communication round among independent workers, and \emph{mini-batch averaging} i.e., communicating at every step. We also provide adaptive lower bounds on the communication frequency for large step-sizes ($ t^{-\alpha} $, $ \alpha\in (1/2 , 1 ) $) and show that \emph{Local-SGD} reduces communication by a factor of $O\Big(\frac{\sqrt{T}}{P^{3/2}}\Big)$, with $T$ the total number of gradients and $P$ machines.


Unsupervised Scalable Representation Learning for Multivariate Time Series

arXiv.org Machine Learning

Time series constitute a challenging data type for machine learning algorithms, due to their highly variable lengths and sparse labeling in practice. In this paper, we tackle this challenge by proposing an unsupervised method to learn universal embeddings of time series. Unlike previous works, it is scalable with respect to their length and we demonstrate the quality, transferability and practicability of the learned representations with thorough experiments and comparisons. To this end, we combine an encoder based on causal dilated convolutions with a triplet loss employing time-based negative sampling, obtaining general-purpose representations for variable length and multivariate time series.


Wasserstein is all you need

arXiv.org Machine Learning

We propose a unified framework for building unsupervised representations of individual objects or entities (and their compositions), by associating with each object both a distributional as well as a point estimate (vector embedding). This is made possible by the use of optimal transport, which allows us to build these associated estimates while harnessing the underlying geometry of the ground space. Our method gives a novel perspective for building rich and powerful feature representations that simultaneously capture uncertainty (via a distributional estimate) and interpretability (with the optimal transport map). As a guiding example, we formulate unsupervised representations for text, in particular for sentence representation and entailment detection. Empirical results show strong advantages gained through the proposed framework. This approach can be used for any unsupervised or supervised problem (on text or other modalities) with a co-occurrence structure, such as any sequence data. The key tools underlying the framework are Wasserstein distances and Wasserstein barycenters (and, hence the title!).


Bridging the Gap between Constant Step Size Stochastic Gradient Descent and Markov Chains

arXiv.org Machine Learning

We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size. While the detailed analysis was only performed for quadratic functions, we provide an explicit asymptotic expansion of the moments of the averaged SGD iterates that outlines the dependence on initial conditions, the effect of noise and the step-size, as well as the lack of convergence in the general (non-quadratic) case. For this analysis, we bring tools from Markov chain theory into the analysis of stochastic gradient and create new ones (similar but different from stochastic MCMC methods). We then show that Richardson-Romberg extrapolation may be used to get closer to the global optimum and we show empirical improvements of the new extrapolation scheme.


Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression

arXiv.org Machine Learning

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first algorithm that achieves jointly the optimal prediction error rates for least-squares regression, both in terms of forgetting of initial conditions in O(1/n 2), and in terms of dependence on the noise and dimension d of the problem, as O(d/n). Our new algorithm is based on averaged accelerated regularized gradient descent, and may also be analyzed through finer assumptions on initial conditions and the Hessian matrix, leading to dimension-free quantities that may still be small while the " optimal " terms above are large. In order to characterize the tightness of these new bounds, we consider an application to non-parametric regression and use the known lower bounds on the statistical performance (without computational limits), which happen to match our bounds obtained from a single pass on the data and thus show optimality of our algorithm in a wide variety of particular trade-offs between bias and variance.