We introduce active generation of Pareto sets (A-GPS), a new framework for online discrete black-box multi-objective optimization (MOO). A-GPS learns a generative model of the Pareto set that supports a-posteriori conditioning on user preferences. The method employs a class probability estimator (CPE) to predict non-dominance relations and to condition the generative model toward high-performing regions of the search space. We also show that this non-dominance CPE implicitly estimates the probability of hypervolume improvement (PHVI). To incorporate subjective trade-offs, A-GPS introduces preference direction vectors that encode user-specified preferences in objective space. At each iteration, the model is updated using both Pareto membership and alignment with these preference directions, producing an amortized generative model capable of sampling across the Pareto front without retraining. The result is a simple yet powerful approach that achieves high-quality Pareto set approximations, avoids explicit hypervolume computation, and flexibly captures user preferences. Empirical results on synthetic benchmarks and protein design tasks demonstrate strong sample efficiency and effective preference incorporation.

翻译：本文提出了帕累托集合主动生成（A-GPS）框架，这是一种用于在线离散黑盒多目标优化（MOO）的新方法。A-GPS学习一个支持后验条件下基于用户偏好调节的帕累托集合生成模型。该方法采用类别概率估计器（CPE）来预测非支配关系，并引导生成模型朝向搜索空间中高性能区域。我们还证明了这种非支配性CPE隐式地估计了超体积改进概率（PHVI）。为纳入主观权衡，A-GPS引入了偏好方向向量，用于在目标空间中编码用户指定的偏好。在每次迭代中，模型通过帕累托隶属度与偏好方向对齐度进行更新，从而得到一个摊销式生成模型，能够在无需重新训练的情况下跨帕累托前沿采样。该方法形成了一种简洁而强大的框架，能够获得高质量的帕累托集合近似，避免显式的超体积计算，并灵活捕捉用户偏好。在合成基准测试和蛋白质设计任务上的实证结果表明，该方法具有出色的样本效率和有效的偏好整合能力。