相关论文: Explicit error bounds for randomized Smolyak algor…
In this paper, we design, analyze, and implement a variant of the two-loop L-shaped algorithms for solving two-stage stochastic programming problems that arise from important application areas including revenue management and power systems.…
Stochastic rounding (SR) is a probabilistic rounding mode that mitigates errors in large-scale numerical computations, especially when prone to stagnation effects. Beyond numerical analysis, SR has shown significant benefits in practical…
Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together. Among various clustering methods, the Minimum Sum-of-Squares Clustering (MSSC) is one of the most widely used. MSSC…
This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical…
We address the problem of solving strongly convex and smooth minimization problems using stochastic gradient descent (SGD) algorithm with a constant step size. Previous works suggested to combine the Polyak-Ruppert averaging procedure with…
Statistical machine learning models trained with stochastic gradient algorithms are increasingly being deployed in critical scientific applications. However, computing the stochastic gradient in several such applications is highly expensive…
Two-time-scale stochastic approximation (SA) is an algorithm with coupled iterations which has found broad applications in reinforcement learning, optimization and game control. In this work, we derive mean squared error bounds for…
Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its…
We study the complexity of randomized computation of integrals depending on a parameter, with integrands from Sobolev spaces. That is, for $r,d_1,d_2\in{\mathbb N}$, $1\le p,q\le \infty$, $D_1= [0,1]^{d_1}$, and $D_2= [0,1]^{d_2}$ we are…
The randomized singular value decomposition proposed in [27] has certainly become one of the most well-established randomization-based algorithms in numerical linear algebra. The key ingredient of the entire procedure is the computation of…
Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…
In large-scale, data-driven applications, parameters are often only known approximately due to noise and limited data samples. In this paper, we focus on high-dimensional optimization problems with linear constraints under uncertain…
Random embedding has been applied with empirical success to large-scale black-box optimization problems with low effective dimensions. This paper proposes the EmbeddedHunter algorithm, which incorporates the technique in a hierarchical…
This work considers a weighted POD-greedy method to estimate statistical outputs parabolic PDE problems with parametrized random data. The key idea of weighted reduced basis methods is to weight the parameter-dependent error estimate…
We analyze the complexity of biased stochastic gradient methods (SGD), where individual updates are corrupted by deterministic, i.e. biased error terms. We derive convergence results for smooth (non-convex) functions and give improved rates…
We study weighted Tikhonov regularization for large-scale linear discrete ill-posed problems with random noise. Under a polynomial upper-bound assumption on the generalized eigenvalues of the discrete forward operator, we derive stochastic…
We show that a very simple randomised algorithm for numerical integration can produce a near optimal rate of convergence for integrals of functions in the $d$-dimensional weighted Korobov space. This algorithm uses a lattice rule with a…
A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…