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Smooth finite-sum optimization has been widely studied in both convex and nonconvex settings.
Probabilistic computations: Toward a unified measure of complexity
Yao, A. C.-C · 1977
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A method for solving the convex programming problem with convergence rate o ( 1 / k s p 2 ) o(1/ksp{2})
Nesterov, Y. E · 1983
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Some np-complete problems in quadratic and nonlinear programming
Murty, K. G · 1987
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A stochastic gradient method with an exponential convergence _rate for finite training sets
Roux, N. L · 2012
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Accelerating stochastic gradient descent using predictive variance reduction
Johnson, R · 2013
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Introductory lectures on convex optimization: A basic course
Nesterov, Y · 2013
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Saga: A fast incremental gradient method with support for non-strongly convex composite objectives
Defazio, A · 2014
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A lower bound for the optimization of finite sums
Agarwal, A · 2015
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Incremental majorization-minimization optimization with application to large-scale machine learning
Mairal, J · 2015
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Shalev-Shwartz, S · 2015
Cited alongside, same era.
Lazysvd: Even faster svd decomposition yet without agonizing pain
Allen-Zhu, Z · 2016
Cited alongside, same era.
Dimension-free iteration complexity of finite sum optimization problems
Arjevani, Y · 2016
Cited alongside, same era.
Faster eigenvector computation via shift-and-invert preconditioning
Garber, D · 2016
Cited alongside, same era.
Sdca without duality, regularization, and individual convexity
Shalev-Shwartz, S · 2016
Cited alongside, same era.
Tight complexity bounds for optimizing composite objectives
Woodworth, B. E · 2016
Cited alongside, same era.
Stochastic optimization with variance reduction for infinite datasets with finite sum structure
Bietti, A · 2017
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Katyusha x: Practical momentum method for stochastic sum-of-nonconvex optimization
Allen-Zhu, Z · 2018
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Accelerated methods for nonconvex optimization
Carmon, Y · 2018
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Chen, Z · 2018
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Spider: Near-optimal non-convex optimization via stochastic path-integrated differential estimator
Fang, C · 2018
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Finding approximate local minima faster than gradient descent
Agarwal, N · 2017
Cited alongside, same era.
Lower bounds for higher-order convex optimization
Agarwal, N · 2017
Cited alongside, same era.
Katyusha: The first direct acceleration of stochastic gradient methods
Allen-Zhu, Z
Cited in the paper.
Natasha: Faster non-convex stochastic optimization via strongly non-convex parameter
Allen-Zhu, Z
Cited in the paper.
Oracle complexity of second-order methods for smooth convex optimization
Arjevani, Y
Cited in the paper.
Lower bounds for finding stationary points i
Carmon, Y
Cited in the paper.
Lan, G · 2018
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Stochastic nested variance reduced gradient descent for nonconvex optimization
Zhou, D · 2018
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A proximal stochastic gradient method with progressive variance reduction
Xiao, L · 2075
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