How Robust is UOBYQA to Worsening, Frozen Noise? Investigations on the bbob Test Suite With Outliers

UOBYQA, short for Unconstrained Optimization By Quadratic Approximation, is one of the well-known solvers derived and implemented by Michael J. D. Powell. In each step, the algorithm builds a quadratic surrogate of the objective function, interpolating quadratically many points for which the true function values are known. The model is optimized within the so-called trust region and the resulting solution is evaluated next. Adaptation of the trust region radius allows for fast convergence on a wide range of (noiseless) functions without the need for derivatives. In this workshop paper, we investigate the effect of (frozen) non-negative, i.e., worsening noise on UOBYQA with varying probability of solutions being affected by the noise. To this end, we use the COCO platform and its newest addition, the noiser, applied to the classical bbob functions. The numerical benchmarking experiments showcase that UOBYQA is negatively affected by the noise, but surprisingly little over a wide range of noise strengths for some of the bbob functions.