Abstract
Stochastic gradient-based optimization methods, such as L-SVRG and its accelerated variant L-Katyusha [12], are widely used to train machine learning models. Theoretical and empirical performance of L-SVRG and L-Katyusha can be improved by sampling the observations from a non-uniform distribution [17]. However, to design a desired sampling distribution, Qian et al.[17] rely on prior knowledge of smoothness constants that can be computationally intractable to obtain in practice when the dimension of the model parameter is high. We propose an adaptive sampling strategy for L-SVRG and L-Katyusha that learns the sampling distribution with little computational overhead, while allowing it to change with iterates, and at the same time does not require any prior knowledge on the problem parameters. We prove convergence guarantees for L-SVRG and L-Katyusha for convex objectives when the sampling distribution changes with iterates. These results show that even without prior information, the proposed adaptive sampling strategy matches, and in some cases even surpasses, the performance of the sampling scheme in Qian et al.[17]. Extensive simulations support our theory and the practical utility of the proposed sampling scheme on real data.
Boxin Zhao
PhD student
Boxin Zhao is a PhD student in Econometrics and Statistics at University of Chicago, Booth School of Business. His research interests include probabilistic graphical models, functional data analysis and distributed learning, with a focus on developing novel methodologies with both practical applications and theoretical guarantees.
Boxiang Lyu
PhD Student
Boxiang is a PhD student in the Econometrics and Statistics dissertation area at University of Chicago Booth School of Business. Prior to coming to Booth, he obtained a Master of Science in Machine Learning (2019) and a Bachelor of Science in Statistics and Machine Learning (2018) from Carnegie Mellon University.
Mladen Kolar
Associate Professor of Econometrics and Statistics
Mladen Kolar is an Associate Professor of Econometrics and Statistics at the University of Chicago Booth School of Business. His research is focused on high-dimensional statistical methods, graphical models, varying-coefficient models and data mining, driven by the need to uncover interesting and scientifically meaningful structures from observational data.