Timezone: »
We study without-replacement SGD for solving finite-sum optimization problems. Specifically, depending on how the indices of the finite-sum are shuffled, we consider the RandomShuffle (shuffle at the beginning of each epoch) and SingleShuffle (shuffle only once) algorithms. First, we establish minimax optimal convergence rates of these algorithms up to poly-log factors. Notably, our analysis is general enough to cover gradient dominated nonconvex costs, and does not rely on the convexity of individual component functions unlike existing optimal convergence results. Secondly, assuming convexity of the individual components, we further sharpen the tight convergence results for RandomShuffle by removing the drawbacks common to all prior arts: large number of epochs required for the results to hold, and extra poly-log factor gaps to the lower bound.
Author Information
Kwangjun Ahn (MIT)
Chulhee Yun (MIT)
Suvrit Sra (MIT)
Suvrit Sra is a faculty member within the EECS department at MIT, where he is also a core faculty member of IDSS, LIDS, MIT-ML Group, as well as the statistics and data science center. His research spans topics in optimization, matrix theory, differential geometry, and probability theory, which he connects with machine learning --- a key focus of his research is on the theme "Optimization for Machine Learning” (http://opt-ml.org)
Related Events (a corresponding poster, oral, or spotlight)
-
2020 Spotlight: SGD with shuffling: optimal rates without component convexity and large epoch requirements »
Fri Dec 11th 04:10 -- 04:20 AM Room Orals & Spotlights: Optimization
More from the Same Authors
-
2020 Poster: Why are Adaptive Methods Good for Attention Models? »
Jingzhao Zhang · Sai Praneeth Karimireddy · Andreas Veit · Seungyeon Kim · Sashank Reddi · Sanjiv Kumar · Suvrit Sra -
2020 Poster: O(n) Connections are Expressive Enough: Universal Approximability of Sparse Transformers »
Chulhee Yun · Yin-Wen Chang · Srinadh Bhojanapalli · Ankit Singh Rawat · Sashank Reddi · Sanjiv Kumar -
2020 Poster: Towards Minimax Optimal Reinforcement Learning in Factored Markov Decision Processes »
Yi Tian · Jian Qian · Suvrit Sra -
2020 Spotlight: Towards Minimax Optimal Reinforcement Learning in Factored Markov Decision Processes »
Yi Tian · Jian Qian · Suvrit Sra -
2019 Poster: Flexible Modeling of Diversity with Strongly Log-Concave Distributions »
Joshua Robinson · Suvrit Sra · Stefanie Jegelka -
2019 Poster: Are deep ResNets provably better than linear predictors? »
Chulhee Yun · Suvrit Sra · Ali Jadbabaie -
2019 Poster: Small ReLU networks are powerful memorizers: a tight analysis of memorization capacity »
Chulhee Yun · Suvrit Sra · Ali Jadbabaie -
2019 Spotlight: Small ReLU networks are powerful memorizers: a tight analysis of memorization capacity »
Chulhee Yun · Suvrit Sra · Ali Jadbabaie -
2018 Poster: Direct Runge-Kutta Discretization Achieves Acceleration »
Jingzhao Zhang · Aryan Mokhtari · Suvrit Sra · Ali Jadbabaie -
2018 Spotlight: Direct Runge-Kutta Discretization Achieves Acceleration »
Jingzhao Zhang · Aryan Mokhtari · Suvrit Sra · Ali Jadbabaie -
2018 Poster: Exponentiated Strongly Rayleigh Distributions »
Zelda Mariet · Suvrit Sra · Stefanie Jegelka -
2018 Tutorial: Negative Dependence, Stable Polynomials, and All That »
Suvrit Sra · Stefanie Jegelka -
2017 Workshop: OPT 2017: Optimization for Machine Learning »
Suvrit Sra · Sashank J. Reddi · Alekh Agarwal · Benjamin Recht -
2017 Poster: Elementary Symmetric Polynomials for Optimal Experimental Design »
Zelda Mariet · Suvrit Sra -
2017 Poster: Polynomial time algorithms for dual volume sampling »
Chengtao Li · Stefanie Jegelka · Suvrit Sra -
2016 Workshop: OPT 2016: Optimization for Machine Learning »
Suvrit Sra · Francis Bach · Sashank J. Reddi · Niao He -
2016 Poster: Fast Mixing Markov Chains for Strongly Rayleigh Measures, DPPs, and Constrained Sampling »
Chengtao Li · Suvrit Sra · Stefanie Jegelka -
2016 Poster: Kronecker Determinantal Point Processes »
Zelda Mariet · Suvrit Sra -
2016 Poster: Proximal Stochastic Methods for Nonsmooth Nonconvex Finite-Sum Optimization »
Sashank J. Reddi · Suvrit Sra · Barnabas Poczos · Alexander Smola -
2016 Poster: Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifolds »
Hongyi Zhang · Sashank J. Reddi · Suvrit Sra -
2016 Tutorial: Large-Scale Optimization: Beyond Stochastic Gradient Descent and Convexity »
Suvrit Sra · Francis Bach -
2015 Workshop: Optimization for Machine Learning (OPT2015) »
Suvrit Sra · Alekh Agarwal · Leon Bottou · Sashank J. Reddi -
2015 Poster: Matrix Manifold Optimization for Gaussian Mixtures »
Reshad Hosseini · Suvrit Sra -
2015 Poster: On Variance Reduction in Stochastic Gradient Descent and its Asynchronous Variants »
Sashank J. Reddi · Ahmed Hefny · Suvrit Sra · Barnabas Poczos · Alexander Smola -
2014 Workshop: OPT2014: Optimization for Machine Learning »
Zaid Harchaoui · Suvrit Sra · Alekh Agarwal · Martin Jaggi · Miro Dudik · Aaditya Ramdas · Jean Lasserre · Yoshua Bengio · Amir Beck -
2014 Poster: Efficient Structured Matrix Rank Minimization »
Adams Wei Yu · Wanli Ma · Yaoliang Yu · Jaime Carbonell · Suvrit Sra -
2013 Workshop: OPT2013: Optimization for Machine Learning »
Suvrit Sra · Alekh Agarwal -
2013 Poster: Geometric optimisation on positive definite matrices for elliptically contoured distributions »
Suvrit Sra · Reshad Hosseini -
2013 Poster: Reflection methods for user-friendly submodular optimization »
Stefanie Jegelka · Francis Bach · Suvrit Sra -
2012 Workshop: Optimization for Machine Learning »
Suvrit Sra · Alekh Agarwal -
2012 Poster: A new metric on the manifold of kernel matrices with application to matrix geometric means »
Suvrit Sra -
2012 Poster: Scalable nonconvex inexact proximal splitting »
Suvrit Sra -
2011 Workshop: Optimization for Machine Learning »
Suvrit Sra · Stephen Wright · Sebastian Nowozin -
2010 Workshop: Numerical Mathematics Challenges in Machine Learning »
Matthias Seeger · Suvrit Sra -
2010 Workshop: Optimization for Machine Learning »
Suvrit Sra · Sebastian Nowozin · Stephen Wright -
2009 Workshop: Optimization for Machine Learning »
Sebastian Nowozin · Suvrit Sra · S.V.N Vishwanthan · Stephen Wright -
2008 Workshop: Optimization for Machine Learning »
Suvrit Sra · Sebastian Nowozin · Vishwanathan S V N