# Multi-objective Optimization by Learning Space Partitions

arXiv: https://arxiv.org/abs/2110.03173 · HTML: https://mlsanity.com/paper/2110.03173/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 67 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 17 of 17)

- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware](https://mlsanity.com/paper/1812.00332/) (2018)
- [NAS-Bench-201: Extending the Scope of Reproducible Neural Architecture Search](https://mlsanity.com/paper/2001.00326/) (2020)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Evaluating the Search Phase of Neural Architecture Search](https://mlsanity.com/paper/1902.08142/) (2019)
- [Learning Search Space Partition for Black-box Optimization using Monte Carlo Tree Search](https://mlsanity.com/paper/2007.00708/) (2020)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [Sample-Efficient Neural Architecture Search by Learning Action Space](https://mlsanity.com/paper/1906.06832/) (2019)
- [Bayesian Optimization with Exponential Convergence](https://mlsanity.com/paper/1604.01348/) (2016)
- [Bayesian Multi-Scale Optimistic Optimization](https://mlsanity.com/paper/1402.7005/) (2014)
- [Solving Black-Box Optimization Challenge via Learning Search Space Partition for Local Bayesian Optimization](https://mlsanity.com/paper/2012.10335/) (2020)
- [Learning Space Partitions for Path Planning](https://mlsanity.com/paper/2106.10544/) (2021)
- [Parallel Architecture and Hyperparameter Search via Successive Halving and Classification](https://mlsanity.com/paper/1805.10255/) (2018)
- [Derivative free optimization via repeated classification](https://mlsanity.com/paper/1804.03761/) (2018)
- [Adaptive Local Bayesian Optimization Over Multiple Discrete Variables](https://mlsanity.com/paper/2012.03501/) (2020)
- [Cutting plane methods can be extended into nonconvex optimization](https://mlsanity.com/paper/1805.08370/) (2018)

## Built on by (most cited first, 8 of 8)

- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [Three-Way Trade-Off in Multi-Objective Learning: Optimization, Generalization and Conflict-Avoidance](https://mlsanity.com/paper/2305.20057/) (2023)
- [ParetoFlow: Guided Flows in Multi-Objective Optimization](https://mlsanity.com/paper/2412.03718/) (2024)
- [Offline Multi-Objective Optimization](https://mlsanity.com/paper/2406.03722/) (2024)
- [Neural Architecture Search: Two Constant Shared Weights Initialisations](https://mlsanity.com/paper/2302.04406/) (2023)
- [Neural Architecture Search by Learning a Hierarchical Search Space](https://mlsanity.com/paper/2503.21061/) (2025)
- [Controllable Pareto Trade-off between Fairness and Accuracy](https://mlsanity.com/paper/2509.13651/) (2025)
- [Interpretability-Guided Bi-objective Optimization: Aligning Accuracy and Explainability](https://mlsanity.com/paper/2601.00655/) (2026)

## Abstract (arXiv)

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.