On the Robustness of BFGS to Positive and Negative Noise Outliers on the BBOB Test Suite

We investigate the impact of outlier noise on the performance of the scipy.optimize implementation of the quasi-Newton BFGS solver. Using the BBOB testbed corrupted with positive—making solution look worse than what they are—or negative—making solutions look better than what they are—outliers simulated with a Cauchy distribution with a probability p, we analyze how the performance is impacted. We show that the impact of positive or negative noise outliers is almost symmetric, that on simple problems BFGS has some robustness to noise, and that for ill-conditionned problems BFGS appears to fail when p or the dimension is too high.