Approximate Bayesian Computation of Bézier Simplices
This work addresses a domain-specific issue in multi-objective optimization for researchers and practitioners, offering an incremental improvement over existing methods.
The paper tackles the problem of over-fitting in Bézier simplex fitting algorithms for approximating Pareto sets/fronts in multi-objective optimization when sample points are noisy, by extending the model to a probabilistic one using approximate Bayesian computation based on Wasserstein distance. The result shows that the new algorithm converges on finite samples and outperforms deterministic methods on noisy instances.
Bézier simplex fitting algorithms have been recently proposed to approximate the Pareto set/front of multi-objective continuous optimization problems. These new methods have shown to be successful at approximating various shapes of Pareto sets/fronts when sample points exactly lie on the Pareto set/front. However, if the sample points scatter away from the Pareto set/front, those methods often likely suffer from over-fitting. To overcome this issue, in this paper, we extend the Bézier simplex model to a probabilistic one and propose a new learning algorithm of it, which falls into the framework of approximate Bayesian computation (ABC) based on the Wasserstein distance. We also study the convergence property of the Wasserstein ABC algorithm. An extensive experimental evaluation on publicly available problem instances shows that the new algorithm converges on a finite sample. Moreover, it outperforms the deterministic fitting methods on noisy instances.