相关论文: Stein Boltzmann Sampling: A Variational Approach f…

Stein Variational Gradient Descent (SVGD) is a popular sampling algorithm used in various machine learning tasks. It is well known that SVGD arises from a discretization of the kernelized gradient flow of the Kullback-Leibler divergence…

We introduce a new Swarm-Based Gradient Descent (SBGD) method for non-convex optimization. The swarm consists of agents, each is identified with a position, ${\mathbf x}$, and mass, $m$. The key to their dynamics is communication: masses…

Stein variational gradient descent (SVGD) is a non-parametric inference algorithm that evolves a set of particles to fit a given distribution of interest. We analyze the non-asymptotic properties of SVGD, showing that there exists a set of…

Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…

Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…

In this investigation, we propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 m x 180 m block in an urban center based on synthetic measurements. Radioactive decay and detection…

Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization…

Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…

We propose a single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized…

We propose Sobolev-regularized Maximum Mean Discrepancy (SrMMD) gradient flow, a regularized variant of maximum mean discrepancy (MMD) gradient flow based on a gradient penalty on the witness function. The proposed regularization mitigates…

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…

Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging, we…

Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…

Ensembles of deep neural networks have achieved great success recently, but they do not offer a proper Bayesian justification. Moreover, while they allow for averaging of predictions over several hypotheses, they do not provide any…

Bayesian optimization (BO) is an effective technique for black-box optimization. However, its applicability is typically limited to moderate-budget problems due to the cubic complexity of fitting the Gaussian process (GP) surrogate model.…

The computationally-efficient solution of fully non-linear microwave inverse scattering problems (ISPs) is addressed. An innovative System-by-Design (SbD) based method is proposed to enable, for the first time to the best of the authors…

Simultaneous perturbation stochastic approximation (SPSA) is an approach to gradient-free optimization introduced by Spall as a simplification of the approach of Kiefer and Wolfowitz. In many cases the most attractive option is the…

A gradient-free deterministic method is developed to solve global optimization problems for Lipschitz continuous functions defined in arbitrary path-wise connected compact sets in Euclidean spaces. The method can be regarded as granular…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…