  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.
