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Found 23 papers, 4 papers with code
Asymptotic normality and optimality in nonsmooth stochastic approximation
In their seminal work, Polyak and Juditsky showed that stochastic approximation algorithms for solving smooth equations enjoy a central limit theorem.
Clustering a Mixture of Gaussians with Unknown Covariance
We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix.
Active manifolds, stratifications, and convergence to local minima in nonsmooth optimization
We show that the subgradient method converges only to local minimizers when applied to generic Lipschitz continuous and subdifferentially regular functions that are definable in an o-minimal structure.
Escaping strict saddle points of the Moreau envelope in nonsmooth optimization
The main conclusion is that a variety of algorithms for nonsmooth optimization can escape strict saddle points of the Moreau envelope at a controlled rate.
Proximal methods avoid active strict saddles of weakly convex functions
We introduce a geometrically transparent strict saddle property for nonsmooth functions.
From low probability to high confidence in stochastic convex optimization
Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation.
Stochastic algorithms with geometric step decay converge linearly on sharp functions
In this work, we ask whether geometric step decay similarly improves stochastic algorithms for the class of sharp nonconvex problems.
Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence
The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science.
Composite optimization for robust blind deconvolution
The blind deconvolution problem seeks to recover a pair of vectors from a set of rank one bilinear measurements.
Graphical Convergence of Subgradients in Nonconvex Optimization and Learning
We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex.
Global Convergence of EM Algorithm for Mixtures of Two Component Linear Regression
Recent results established that EM enjoys global convergence for Gaussian Mixture Models.
Stochastic model-based minimization under high-order growth
Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function.
Stochastic subgradient method converges on tame functions
This work considers the question: what convergence guarantees does the stochastic subgradient method have in the absence of smoothness and convexity?
Stochastic model-based minimization of weakly convex functions
We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function.
Stochastic subgradient method converges at the rate $O(k^{-1/4})$ on weakly convex functions
We prove that the proximal stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$.
Proximally Guided Stochastic Subgradient Method for Nonsmooth, Nonconvex Problems
In this paper, we introduce a stochastic projected subgradient method for weakly convex (i. e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes.
The Sound of APALM Clapping: Faster Nonsmooth Nonconvex Optimization with Stochastic Asynchronous PALM
We introduce the Stochastic Asynchronous Proximal Alternating Linearized Minimization (SAPALM) method, a block coordinate stochastic proximal-gradient method for solving nonconvex, nonsmooth optimization problems.
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 arises from fitting a machine learning model into one that (1) detects and removes contaminated data from the training set while (2) simultaneously fitting the trimmed model on the uncontaminated data that remains.
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-rank formulations for data interpolation allow practitioners to `fill in' data volumes from critically subsampled data acquired in the field.
Multi-View Feature Engineering and Learning
We frame the problem of local representation of imaging data as the computation of minimal sufficient statistics that are invariant to nuisance variability induced by viewpoint and illumination.
An $O(n\log(n))$ Algorithm for Projecting Onto the Ordered Weighted $\ell_1$ Norm Ball
The ordered weighted $\ell_1$ (OWL) norm is a newly developed generalization of the Octogonal Shrinkage and Clustering Algorithm for Regression (OSCAR) norm.
Asymmetric Sparse Kernel Approximations for Large-scale Visual Search
We introduce an asymmetric sparse approximate embedding optimized for fast kernel comparison operations arising in large-scale visual search.
On the Design and Analysis of Multiple View Descriptors
We propose an extension of popular descriptors based on gradient orientation histograms (HOG, computed in a single image) to multiple views.
