Related papers: Adaptive Finite-Difference Interval Estimation for…

Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…

In this paper, we present a stochastic gradient algorithm for minimizing a smooth objective function that is an expectation over noisy cost samples, and only the latter are observed for any given parameter. Our algorithm employs a gradient…

We prove that the finite-difference based derivative-free descent (FD-DFD) methods have a capability to find the global minima for a class of multiple minima problems. Our main result shows that, for a class of multiple minima objectives…

This paper is devoted to the numerical analysis of a fully discrete finite element approximation for the stochastic Benjamin-Bona-Mahony equation driven by multiplicative noise. We first establish the existence and uniqueness of solutions…

Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are effective in the small-noise regime are suboptimal…

We propose a novel algorithm that extends the methods of ball smoothing and Gaussian smoothing for noisy derivative-free optimization by accounting for the heterogeneous curvature of the objective function. The algorithm dynamically adapts…

We propose a derivative-free trust-region method based on finite-difference gradient approximations for smooth optimization problems with convex constraints. The proposed method does not require computing an approximate stationarity…

A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…

A new paradigm to estimate the gradient of a black-box scalar function is introduced, considering it as a member of a set of admissible gradients that are computed using existing function samples. Results on gradient estimate accuracy,…

A numerical model based on the finite-difference time-domain method is developed to simulate fluctuations which accompany the dephasing of atomic polarization and the decay of excited state's population. This model is based on the…

Recently, several studies consider the stochastic optimization problem but in a heavy-tailed noise regime, i.e., the difference between the stochastic gradient and the true gradient is assumed to have a finite $p$-th moment (say being upper…

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

We deal with pointwise approximation of solutions of scalar stochastic differential equations in the presence of informational noise about underlying drift and diffusion coefficients. We define a randomized derivative-free version of…

This paper proposes a new framework to compute finite-horizon safety guarantees for discrete-time piece-wise affine systems with stochastic noise of unknown distributions. The approach is based on a novel approach to synthesise a stochastic…

We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on…

This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery…

In this paper, we consider the problem of estimating finite rate of innovation (FRI) signals from noisy measurements, and specifically analyze the interaction between FRI techniques and the underlying sampling methods. We first obtain a…

While local basis function (LBF) estimation algorithms, commonly used for identifying/tracking systems with time-varying parameters, demonstrate good performance under the assumption of normally distributed measurement noise, the estimation…

We develop a framework for efficiently transforming certain approximation algorithms into differentially-private variants, in a black-box manner. Specifically, our results focus on algorithms A that output an approximation to a function f…

In this work we consider unconstrained optimization problems. The objective function is known through a zeroth order stochastic oracle that gives an estimate of the true objective function. To solve these problems, we propose a…