Bézier单纯形的近似贝叶斯计算
Approximate Bayesian Computation of Bézier Simplices
摘要：
最近提出了Bézier单纯形拟合算法来逼近多目标连续优化问题的Pareto集/前沿。这些新的方法已被证明是成功的近似各种形状的帕累托集/阵线时，样本点正好位于帕累托集/阵线。然而，如果样本点远离Pareto集合/前沿，则这些方法通常可能遭受过拟合。为了克服这个问题，本文将Bézier单纯形模型扩展为概率模型，并提出了一种新的Bézier单纯形模型的学习算法，该算法属于基于Wasserstein距离的近似贝叶斯计算（ABC）框架。我们还研究了Wasserstein ABC算法的收敛性。对公开问题实例的广泛实验评估表明，新算法在有限样本上收敛。此外，它优于噪声情况下的确定性拟合方法。
英文摘要：
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.
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