120 citations · 154 across the 17 of their papers we have counts for
19 papers
Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing
Hoang Tran, Qiang Du, Guannan Zhang
We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is pr…
Differentially Private Online-to-Batch for Smooth Losses
Qinzi Zhang, Hoang Tran, Ashok Cutkosky
We develop a new reduction that converts any online convex optimization algorithm suffering regret into an -differentially private stochastic convex optimization a…
Momentum Aggregation for Private Non-convex ERM
Hoang Tran, Ashok Cutkosky
We introduce new algorithms and convergence guarantees for privacy-preserving non-convex Empirical Risk Minimization (ERM) on smooth -dimensional objectives. We develop an impro…
Compressive-sensing-assisted mixed integer optimization for dynamical system discovery with highly noisy data
Zhongshun Shi, Hang Ma, Hoang Tran +1
The identification of governing equations for dynamical systems is everlasting challenges for the fundamental research in science and engineering. Machine learning has exhibited gr…
Better SGD using Second-order Momentum
Hoang Tran, Ashok Cutkosky
We develop a new algorithm for non-convex stochastic optimization that finds an -critical point in the optimal stochastic gradient and Hessian-vector product computa…
AdaDGS: An adaptive black-box optimization method with a nonlocal directional Gaussian smoothing gradient
Hoang Tran, Guannan Zhang
The local gradient points to the direction of the steepest slope in an infinitesimal neighborhood. An optimizer guided by the local gradient is often trapped in local optima when t…
Analysis of The Ratio of and Norms in Compressed Sensing
Yiming Xu, Akil Narayan, Hoang Tran +1
We first propose a novel criterion that guarantees that an -sparse signal is the local minimizer of the objective; our criterion is interpretable and useful in p…
Accelerating Reinforcement Learning with a Directional-Gaussian-Smoothing Evolution Strategy
Jiaxing Zhang, Hoang Tran, Guannan Zhang
Evolution strategy (ES) has been shown great promise in many challenging reinforcement learning (RL) tasks, rivaling other state-of-the-art deep RL methods. Yet, there are two limi…
A Novel Evolution Strategy with Directional Gaussian Smoothing for Blackbox Optimization
Jiaxin Zhang, Hoang Tran, Dan Lu +1
We propose an improved evolution strategy (ES) using a novel nonlocal gradient operator for high-dimensional black-box optimization. Standard ES methods with -dimensional Gaussi…
Reconstructing high-dimensional Hilbert-valued functions via compressed sensing
Nick Dexter, Hoang Tran, Clayton Webster
We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equat…
On Cross-validation for Sparse Reduced Rank Regression
Yiyuan She, Hoang Tran
In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it i…
A mixed regularization approach for sparse simultaneous approximation of parameterized PDEs
Nick Dexter, Hoang Tran, Clayton Webster
We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochast…
Reconstruction of jointly sparse vectors via manifold optimization
Armenak Petrosyan, Hoang Tran, Clayton Webster
In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we…
Analysis of sparse recovery for Legendre expansions using envelope bound
Hoang Tran, Clayton Webster
We provide novel sufficient conditions for the uniform recovery of sparse Legendre expansions using minimization, where the sampling points are drawn according to orthogon…
On the strong convergence of forward-backward splitting in reconstructing jointly sparse signals
Nick Dexter, Hoang Tran, Clayton Webster
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in cont…
A class of null space conditions for sparse recovery via nonconvex, non-separable minimizations
Hoang Tran, Clayton Webster
For the problem of sparse recovery, it is widely accepted that nonconvex minimizations are better than penalty in enhancing the sparsity of solution. However, to date, the…
Polynomial approximation via compressed sensing of high-dimensional functions on lower sets
Abdellah Chkifa, Nick Dexter, Hoang Tran +1
This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting wher…
Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients
Hoang Tran, Clayton G. Webster, Guannan Zhang
In this work, we present a generalized methodology for analyzing the convergence of quasi-optimal Taylor and Legendre approximations, applicable to a wide class of parameterized el…
A sparse grid method for Bayesian uncertainty quantification with application to large eddy simulation turbulence models
Hoang A. Tran, Clayton G. Webster, Guannan Zhang
There is wide agreement that the accuracy of turbulence models suffer from their sensitivity with respect to physical input data, the uncertainties of user-elected parameters, as w…