Pareto front learning is a technique that introduces preference vectors in a
neural network to approximate the Pareto front. Previous Pareto front learning
methods have demonstrated high performance in approximating simple Pareto
fronts. These methods often sample preference vectors from a fixed Dirichlet
distribution. However, no fixed sampling distribution can be adapted to diverse
Pareto fronts. Efficiently sampling preference vectors and accurately
estimating the Pareto front is a challenge. To address this challenge, we
propose a data-driven preference vector sampling framework for Pareto front
learning. We utilize the posterior information of the objective functions to
adjust the parameters of the sampling distribution flexibly. In this manner,
the proposed method can sample preference vectors from the location of the
Pareto front with a high probability. Moreover, we design the distribution of
the preference vector as a mixture of Dirichlet distributions to improve the
performance of the model in disconnected Pareto fronts. Extensive experiments
validate the superiority of the proposed method compared with state-of-the-art
algorithms.

通过数据驱动的偏好向量采样框架，灵活地调整采样分布参数，从而实现高概率从 Pareto 前沿位置采样偏好向量，并且通过使用混合狄利克雷分布来改进模型在不连通 Pareto 前沿中的性能。

基于数据驱动的 Pareto 前缘学习的偏好采样

Data-Driven Preference Sampling for Pareto Front Learning

Pareto Front Learning (PFL) was recently introduced as an effective approach
to obtain a mapping function from a given trade-off vector to a solution on the
Pareto front, which solves the multi-objective optimization (MOO) problem. Due
to the inherent trade-off between conflicting objectives, PFL offers a flexible
approach in many scenarios in which the decision makers can not specify the
preference of one Pareto solution over another, and must switch between them
depending on the situation. However, existing PFL methods ignore the
relationship between the solutions during the optimization process, which
hinders the quality of the obtained front. To overcome this issue, we propose a
novel PFL framework namely PHN-HVI, which employs a hypernetwork to generate
multiple solutions from a set of diverse trade-off preferences and enhance the
quality of the Pareto front by maximizing the Hypervolume indicator defined by
these solutions. The experimental results on several MOO machine learning tasks
show that the proposed framework significantly outperforms the baselines in
producing the trade-off Pareto front.

提出 PHN-HVI 框架，利用超网络从多样化的权衡偏好生成多个解并最大化这些解定义的超体积指标以提高 Pareto 前沿的质量，在多个 MOO 机器学习任务上实验结果表明，与基线方法相比，该框架显著提高了产生权衡 Pareto 前沿的性能。