7 citations · 14 across the 5 of their papers we have counts for
5 papers · 1 filter
The Error in Multivariate Linear Extrapolation with Applications to Derivative-Free Optimization
Liyuan Cao, Zaiwen Wen, Ya-xiang Yuan
We study in this paper the function approximation error of multivariate linear extrapolation. The sharp error bound of linear interpolation already exists in the literature. Howeve…
First- and Second-Order High Probability Complexity Bounds for Trust-Region Methods with Noisy Oracles
Liyuan Cao, Albert S. Berahas, Katya Scheinberg
In this paper, we present convergence guarantees for a modified trust-region method designed for minimizing objective functions whose value and gradient and Hessian estimates are c…
Global Convergence Rate Analysis of a Generic Line Search Algorithm with Noise
Albert S. Berahas, Liyuan Cao, Katya Scheinberg
In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact…
Linear interpolation gives better gradients than Gaussian smoothing in derivative-free optimization
Albert S Berahas, Liyuan Cao, Krzysztof Choromanski +1
In this paper, we consider derivative free optimization problems, where the objective function is smooth but is computed with some amount of noise, the function evaluations are exp…
A Theoretical and Empirical Comparison of Gradient Approximations in Derivative-Free Optimization
Albert S. Berahas, Liyuan Cao, Krzysztof Choromanski +1
In this paper, we analyze several methods for approximating gradients of noisy functions using only function values. These methods include finite differences, linear interpolation,…