Related papers: Convergence rates of efficient global optimization…
Quantifying the data uncertainty in learning tasks is often done by learning a prediction interval or prediction set of the label given the input. Two commonly desired properties for learned prediction sets are \emph{valid coverage} and…
A fundamental problem in statistics and machine learning is to estimate a function $f$ from possibly noisy observations of its point samples. The goal is to design a numerical algorithm to construct an approximation $\hat f$ to $f$ in a…
In this work, we propose a computationally efficient algorithm for the problem of global optimization in univariate loss functions. For the performance evaluation, we study the cumulative regret of the algorithm instead of the simple regret…
Bayesian optimization is a sample-efficient method for finding a global optimum of an expensive-to-evaluate black-box function. A global solution is found by accumulating a pair of query point and its function value, repeating these two…
This paper studies the fixed budget formulation of the Ranking and Selection (R&S) problem with independent normal samples, where the goal is to investigate different algorithms' convergence rate in terms of their resulting probability of…
Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…
Machine learning algorithms typically perform optimization over a class of non-convex functions. In this work, we provide bounds on the fundamental hardness of identifying the global minimizer of a non convex function. Specifically, we…
Finding the global minimum of non-convex functions is one of the main and most difficult problems in modern optimization. In the first part of the paper, we consider a certain class of "good" non-convex functions that can be bounded above…
Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
Finding global optima in high-dimensional optimization problems is extremely challenging since the number of function evaluations required to sufficiently explore the search space increases exponentially with its dimensionality.…
We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…
The advancement of artificial intelligence has cast a new light on the development of optimization algorithm. This paper proposes to learn a two-phase (including a minimization phase and an escaping phase) global optimization algorithm for…
In this article, we extend our previous work (Applicable Analysis, 2024, pp. 1-25) on the steepest descent method for uncertain multiobjective optimization problems. While that study established local convergence, it did not address global…
The goal of this paper is to characterize Gaussian-Process optimization in the setting where the function domain is large relative to the number of admissible function evaluations, i.e., where it is impossible to find the global optimum. We…
Making use of predictions is a crucial, but under-explored, area of online algorithms. This paper studies a class of online optimization problems where we have external noisy predictions available. We propose a stochastic prediction error…
First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
In this work, we propose an efficient minimax optimal global optimization algorithm for multivariate Lipschitz continuous functions. To evaluate the performance of our approach, we utilize the average regret instead of the traditional…
We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…