The construction of machine learning models involves many bi-level multi-objective optimization problems (BL-MOPs), where upper level (UL) candidate solutions must be evaluated via training weights of a model in the lower level (LL). Due to the Pareto optimality of sub-problems and the complex dependency across UL solutions and LL weights, an UL solution is feasible if and only if the LL weight is Pareto optimal. It is computationally expensive to determine which LL Pareto weight in the LL Pareto weight set is the most appropriate for each UL solution. This paper proposes a bi-level multi-objective learning framework (BLMOL), coupling the above decision-making process with the optimization process of the UL-MOP by introducing LL preference $r$. Specifically, the UL variable and $r$ are simultaneously searched to minimize multiple UL objectives by evolutionary multi-objective algorithms. The LL weight with respect to $r$ is trained to minimize multiple LL objectives via gradient-based preference multi-objective algorithms. In addition, the preference surrogate model is constructed to replace the expensive evaluation process of the UL-MOP. We consider a novel case study on multi-task graph neural topology search. It aims to find a set of Pareto topologies and their Pareto weights, representing different trade-offs across tasks at UL and LL, respectively. The found graph neural network is employed to solve multiple tasks simultaneously, including graph classification, node classification, and link prediction. Experimental results demonstrate that BLMOL can outperform some state-of-the-art algorithms and generate well-representative UL solutions and LL weights.

翻译：机器学习模型的构建涉及许多双层多目标优化问题（BL-MOPs），其中上层（UL）候选解必须通过下层（LL）模型权重的训练来评估。由于子问题的帕累托最优性以及上层解与下层权重之间的复杂依赖关系，当且仅当下层权重是帕累托最优时，上层解才是可行的。确定下层帕累托权重集中的哪一个最适用于每个上层解，在计算上具有很高的代价。本文提出了一种双层多目标学习框架（BLMOL），通过引入下层偏好$r$，将上述决策过程与上层多目标优化（UL-MOP）的优化过程相结合。具体而言，UL变量和$r$通过进化多目标算法同时进行搜索，以最小化多个UL目标；与$r$对应的下层权重通过基于梯度的偏好多目标算法进行训练，以最小化多个LL目标。此外，构建偏好代理模型以替代UL-MOP昂贵的评估过程。我们以多任务图神经拓扑搜索为例进行案例研究，旨在找到一组帕累托拓扑结构及其帕累托权重，分别表示UL层面和LL层面任务间的不同权衡。所发现的图神经网络用于同时解决多个任务，包括图分类、节点分类和链接预测。实验结果表明，BLMOL能够优于一些最先进的算法，并生成具有代表性的UL解和LL权重。