Polynomial-Model-Based Optimization for Blackbox Objectives
This addresses optimization problems for systems with unknown structures, such as neural networks or simulations, but appears incremental as it builds on Bayesian optimization with a polynomial model.
The paper tackles black-box optimization by proposing Polynomial-Model-Based Optimization (PMBO), which fits a polynomial surrogate to the objective function and uses an acquisition function for iterative updates; it competes successfully with state-of-the-art algorithms and outperforms them in some cases on artificial, analytical functions.
For a wide range of applications the structure of systems like Neural Networks or complex simulations, is unknown and approximation is costly or even impossible. Black-box optimization seeks to find optimal (hyper-) parameters for these systems such that a pre-defined objective function is minimized. Polynomial-Model-Based Optimization (PMBO) is a novel blackbox optimizer that finds the minimum by fitting a polynomial surrogate to the objective function. Motivated by Bayesian optimization the model is iteratively updated according to the acquisition function Expected Improvement, thus balancing the exploitation and exploration rate and providing an uncertainty estimate of the model. PMBO is benchmarked against other state-of-the-art algorithms for a given set of artificial, analytical functions. PMBO competes successfully with those algorithms and even outperforms all of them in some cases. As the results suggest, we believe PMBO is the pivotal choice for solving blackbox optimization tasks occurring in a wide range of disciplines.