Active Learning for Approximation of Expensive Functions with Normal Distributed Output Uncertainty

TL;DR

This paper introduces an enhanced active learning method for approximating expensive black-box functions, accounting for output uncertainty to improve sampling efficiency and model accuracy.

Contribution

It extends the FLOLA-Voronoi active learning algorithm to handle output uncertainty, emphasizing exploration to better inform models of complex functions.

Findings

The method effectively balances exploration and exploitation in uncertain environments.

Increased sampling in uncertain regions improves approximation accuracy.

Theoretical analysis clarifies the impact of output uncertainty on active learning.

Abstract

When approximating a black-box function, sampling with active learning focussing on regions with non-linear responses tends to improve accuracy. We present the FLOLA-Voronoi method introduced previously for deterministic responses, and theoretically derive the impact of output uncertainty. The algorithm automatically puts more emphasis on exploration to provide more information to the models.