In contrast to single-objective optimization (SOO), multi-objective optimization (MOO) requires an optimizer to find the Pareto frontier, a subset of feasible solutions that are not dominated by other feasible solutions. In this paper, we propose LaMOO, a novel multi-objective optimizer that learns a model from observed samples to partition the search space and then focus on promising regions that are likely to contain a subset of the Pareto frontier. The partitioning is based on the dominance number, which measures "how close" a data point is to the Pareto frontier among existing samples. To account for possible partition errors due to limited samples and model mismatch, we leverage Monte Carlo Tree Search (MCTS) to exploit promising regions while exploring suboptimal regions that may turn out to contain good solutions later. Theoretically, we prove the efficacy of learning space partitioning via LaMOO under certain assumptions. Empirically, on the HyperVolume (HV) benchmark, a popular MOO metric, LaMOO substantially outperforms strong baselines on multiple real-world MOO tasks, by up to 225% in sample efficiency for neural architecture search on Nasbench201, and up to 10% for molecular design.
翻译:与单一目标优化(SOO)相比,多目标优化(MOO)要求优化者找到Pareto边界,这是一系列可行的解决办法,而其他可行的解决办法并不主导。在本文件中,我们提议拉MOO,这是一个全新的多目标优化器,从观测到的样本中学习模型,以分割搜索空间,然后侧重于有可能包含Pareto边界子的有前景的区域。分割以主导数为基础,即测量数据点“如何接近”于现有样品中的Pareto边界。为了说明由于样本有限和模型不匹配而可能造成的分区差错,我们利用MCTS(MCTS)利用充满希望的区域,同时探索将来可能含有良好解决办法的亚最佳区域。理论上,我们证明在某些假设下通过LaMOO学习空间分割的功效。根据超波罗姆(HV)基准,即流行的MOO测量值,LaMOO大大超出多个实际MOO任务的强基线,在样本效率方面达到225 %,用于Nasbench1的分子结构设计1020。