不确定性下多目标优化的期望超体积最大化

中文摘要 AI 辅助

在不确定性下的多目标优化问题通常通过对每个目标取期望来处理。在本工作中，我们提出将其表述为一个贝叶斯决策问题，并依赖于超体积的期望值，该期望值相对于一组有限的输入点进行最大化。我们表明，在随机优化框架中，只要对支配点加以注意，就可以使用基于梯度的方法来执行此操作。此外，在没有现成可微代码的情况下，我们建议使用高斯过程作为可微的替代模型以执行优化。本工作的另一个贡献是一些主动学习策略，通过采集函数帮助构建一个针对所研究的多目标优化问题设计良好的替代模型。这些策略在简单的解析问题上进行了比较以评估其性能。

英文摘要

The problem of multiobjective optimization under uncertainties is often approached by taking the expectation of each objective. In this work, we propose instead to formulate this as a Bayesian decision problem and to rely on the expected value of the hypervolume, which is to be maximized with respect to a finite set of input points. We show that this can be performed using methods based on gradients in a stochastic optimization framework, provided that care is taken with respect to dominated points. Moreover, in the absence of readily available differentiable code, we propose to use Gaussian Processes as differentiable surrogate models, in order to perform the optimization. An additional contribution in this work are some active learning strategies, through acquisition functions which helps construct a surrogate model well-designed for the multiobjective optimization problem at stake. These strategies are compared on simple analytical problems to assess their performances.

发表机构

• CNRS, UMR 6158 LIMOS（法国国家科学研究中心，LIMOS混合研究单位6158）

机构由 AI 辅助整理，请以论文原文为准。