SACOBRA with Online Whitening for Solving Optimization Problems with High Conditioning
This work addresses a specific bottleneck in surrogate-assisted optimization for expensive real-world problems, offering an incremental improvement to handle high-conditioning issues.
The paper tackled the challenge of optimizing expensive functions with high condition numbers by proposing an online whitening method for the SACOBRA surrogate-assisted optimizer, which reduced optimization error by factors between 10 to 1e12 compared to plain SACOBRA on high-conditioning functions, though with extra function evaluations.
Real-world optimization problems often have expensive objective functions in terms of cost and time. It is desirable to find near-optimal solutions with very few function evaluations. Surrogate-assisted optimizers tend to reduce the required number of function evaluations by replacing the real function with an efficient mathematical model built on few evaluated points. Problems with a high condition number are a challenge for many surrogate-assisted optimizers including SACOBRA. To address such problems we propose a new online whitening operating in the black-box optimization paradigm. We show on a set of high-conditioning functions that online whitening tackles SACOBRA's early stagnation issue and reduces the optimization error by a factor between 10 to 1e12 as compared to the plain SACOBRA, though it imposes many extra function evaluations. Covariance matrix adaptation evolution strategy (CMA-ES) has for very high numbers of function evaluations even lower errors, whereas SACOBRA performs better in the expensive setting (less than 1e03 function evaluations). If we count all parallelizable function evaluations (population evaluation in CMA-ES, online whitening in our approach) as one iteration, then both algorithms have comparable strength even on the long run. This holds for problems with dimension D <= 20.