相关论文: Stochastic Average Model Methods

We consider the problem of minimizing the sum of an average function of a large number of smooth convex components and a general, possibly non-differentiable, convex function. Although many methods have been proposed to solve this problem…

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…

We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on…

This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic…

This paper introduces a practical sampling method for training surrogate models in the context of uncertainty propagation. We propose a heuristic method to uniformly draw samples within highest density regions of the density given by the…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

Promptable foundation models, particularly Segment Anything Model (SAM), have emerged as a promising alternative to the traditional task-specific supervised learning for image segmentation. However, many evaluation studies have found that…

Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or…

In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides…

We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives…

Two of the principle tasks of causal inference are to define and estimate the effect of a treatment on an outcome of interest. Formally, such treatment effects are defined as a possibly functional summary of the data generating…

Segment Anything Model (SAM) is a foundation model for semantic segmentation and shows excellent generalization capability with the prompts. In this empirical study, we investigate the robustness and zero-shot generalizability of the SAM in…

The paper investigates the fundamental convergence properties of Sharpness-Aware Minimization (SAM), a recently proposed gradient-based optimization method [Foret et al., 2021] that significantly improves the generalization of deep neural…

This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…

This paper investigates solving convex composite optimization on an undirected network, where each node, privately endowed with a smooth component function and a nonsmooth one, is required to minimize the sum of all the component functions…

The Segment Anything Model (SAM) is a foundation model for general image segmentation. Although it exhibits impressive performance predominantly on natural images, understanding its robustness against various image perturbations and domains…

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal values and empirical…

In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through…