285 citations · 499 across the 55 of their papers we have counts for
7 papers · 2 filters
Local Convergence of Adaptively Regularized Tensor Methods
Karl Welzel, Yang Liu, Raphael A. Hauser +1
Optimization methods that make use of derivatives of the objective function up to order are called tensor methods. Among them, ones that minimize a regularized th-order…
Nonlinear Dimensionality Reduction Techniques for Bayesian Optimization
Luo Long, Coralia Cartis, Paz Fink Shustin
Bayesian optimisation (BO) enables sample-efficient global optimisation of expensive black-box functions but remains challenging in high dimensions. We investigate nonlinear dimens…
On Global Rates for Regularization Methods based on Secant Derivative Approximations
Coralia Cartis, Sadok Jerad, Karl Welzel
An inexact and globally convergent framework for high-order adaptive regularization methods is presented, in which approximations may be used for the th-order tensor, based on l…
Global Optimality Characterizations and Algorithms for Minimizing Quartically-Regularized Third-Order Taylor Polynomials
Wenqi Zhu, Coralia Cartis
High-order methods for convex and nonconvex optimization, particularly th-order Adaptive Regularization Methods (AR), have attracted significant research interest by naturall…
Random Subspace Cubic-Regularization Methods, with Applications to Low-Rank Functions
Coralia Cartis, Zhen Shao, Edward Tansley
We propose and analyze random subspace variants of the second-order Adaptive Regularization using Cubics (ARC) algorithm. These methods iteratively restrict the search space to som…
Scalable Second-Order Optimization Algorithms for Minimizing Low-rank Functions
Edward Tansley, Coralia Cartis
We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix…
Efficient Implementation of Third-Order Tensor Methods with Adaptive Regularization for Unconstrained Optimization
Coralia Cartis, Raphael Hauser, Yang Liu +2
High-order tensor methods that employ local Taylor models of degree within adaptive regularization frameworks (AR) have recently received significant attention, due to their…