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06/05/2023
Aiming towards the minimizers: fast convergence of SGD for overparametrized problems
Modern machine learning paradigms, such as deep learning, occur in or cl...
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01/16/2023
Asymptotic normality and optimality in nonsmooth stochastic approximation
In their seminal work, Polyak and Juditsky showed that stochastic approx...
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10/04/2021
Clustering a Mixture of Gaussians with Unknown Covariance
We investigate a clustering problem with data from a mixture of Gaussian...
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08/26/2021
Subgradient methods near active manifolds: saddle point avoidance, local convergence, and asymptotic normality
Nonsmooth optimization problems arising in practice tend to exhibit bene...
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06/17/2021
Escaping strict saddle points of the Moreau envelope in nonsmooth optimization
Recent work has shown that stochastically perturbed gradient methods can...
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12/16/2019
Active strict saddles in nonsmooth optimization
We introduce a geometrically transparent strict saddle property for nons...
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07/31/2019
Robust stochastic optimization with the proximal point method
Standard results in stochastic convex optimization bound the number of s...
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07/22/2019
Stochastic algorithms with geometric step decay converge linearly on sharp functions
Stochastic (sub)gradient methods require step size schedule tuning to pe...
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04/22/2019
Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence
The task of recovering a low-rank matrix from its noisy linear measureme...
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01/06/2019
Composite optimization for robust blind deconvolution
The blind deconvolution problem seeks to recover a pair of vectors from ...
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10/17/2018
Uniform Graphical Convergence of Subgradients in Nonconvex Optimization and Learning
We investigate the stochastic optimization problem of minimizing populat...
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07/01/2018
Stochastic model-based minimization under high-order growth
Given a nonsmooth, nonconvex minimization problem, we consider algorithm...
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04/20/2018
Stochastic subgradient method converges on tame functions
This work considers the question: what convergence guarantees does the s...
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03/17/2018
Stochastic model-based minimization of weakly convex functions
We consider an algorithm that successively samples and minimizes stochas...
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02/08/2018
Stochastic subgradient method converges at the rate O(k^-1/4) on weakly convex functions
We prove that the projected stochastic subgradient method, applied to a ...
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10/04/2016
A SMART Stochastic Algorithm for Nonconvex Optimization with Applications to Robust Machine Learning
In this paper, we show how to transform any optimization problem that ar...
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07/09/2016
Beating level-set methods for 3D seismic data interpolation: a primal-dual alternating approach
Acquisition cost is a crucial bottleneck for seismic workflows, and low-...
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11/23/2013