Extrapolation methods use the last few iterates of an optimization algorithm to produce a better estimate of the optimum. They were shown to achieve optimal convergence rates in a deterministic setting using simple gradient iterates. Here, we study extrapolation methods in a stochastic setting, where the iterates are produced by either a simple or an accelerated stochastic gradient algorithm. We first derive convergence bounds for arbitrary, potentially biased perturbations, then produce asymptotic bounds using the ratio between the variance of the noise and the accuracy of the current point. Finally, we apply this acceleration technique to stochastic algorithms such as SGD, SAGA, SVRG and Katyusha in different settings, and show significant performance gains.
Author Information
Damien Scieur (INRIA - ENS)
Francis Bach (Inria)
Francis Bach is a researcher at INRIA, leading since 2011 the SIERRA project-team, which is part of the Computer Science Department at Ecole Normale Supérieure in Paris, France. After completing his Ph.D. in Computer Science at U.C. Berkeley, he spent two years at Ecole des Mines, and joined INRIA and Ecole Normale Supérieure in 2007. He is interested in statistical machine learning, and especially in convex optimization, combinatorial optimization, sparse methods, kernel-based learning, vision and signal processing. He gave numerous courses on optimization in the last few years in summer schools. He has been program co-chair for the International Conference on Machine Learning in 2015.
Alexandre d'Aspremont (CNRS - Ecole Normale Supérieure)
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2017 Workshop: (Almost) 50 shades of Bayesian Learning: PAC-Bayesian trends and insights »
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2017 Poster: On Structured Prediction Theory with Calibrated Convex Surrogate Losses »
Anton Osokin · Francis Bach · Simon Lacoste-Julien -
2017 Poster: Sharpness, Restart and Acceleration »
Vincent Roulet · Alexandre d'Aspremont -
2017 Oral: On Structured Prediction Theory with Calibrated Convex Surrogate Losses »
Anton Osokin · Francis Bach · Simon Lacoste-Julien -
2017 Poster: Integration Methods and Optimization Algorithms »
Damien Scieur · Vincent Roulet · Francis Bach · Alexandre d'Aspremont -
2016 Poster: Regularized Nonlinear Acceleration »
Damien Scieur · Alexandre d'Aspremont · Francis Bach -
2016 Oral: Regularized Nonlinear Acceleration »
Damien Scieur · Alexandre d'Aspremont · Francis Bach -
2016 Tutorial: Large-Scale Optimization: Beyond Stochastic Gradient Descent and Convexity »
Suvrit Sra · Francis Bach
