# Covering Multiple Objectives with a Small Set of Solutions Using Bayesian Optimization

arXiv: https://arxiv.org/abs/2501.19342 · HTML: https://mlsanity.com/paper/2501.19342/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 89 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 30 of 39)

- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [NIMA: Neural Image Assessment](https://mlsanity.com/paper/1709.05424/) (2017)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Blind Image Quality Assessment via Vision-Language Correspondence: A Multitask Learning Perspective](https://mlsanity.com/paper/2303.14968/) (2023)
- [TOPIQ: A Top-down Approach from Semantics to Distortions for Image Quality Assessment](https://mlsanity.com/paper/2308.03060/) (2023)
- [No-Reference Image Quality Assessment via Transformers, Relative Ranking, and Self-Consistency](https://mlsanity.com/paper/2108.06858/) (2021)
- [Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020](https://mlsanity.com/paper/2104.10201/) (2021)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1511.05467/) (2015)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [Local Latent Space Bayesian Optimization over Structured Inputs](https://mlsanity.com/paper/2201.11872/) (2022)
- [Parallel and Distributed Thompson Sampling for Large-scale Accelerated Exploration of Chemical Space](https://mlsanity.com/paper/1706.01825/) (2017)
- [High-Dimensional Bayesian Optimisation with Variational Autoencoders and Deep Metric Learning](https://mlsanity.com/paper/2106.03609/) (2021)
- [Improving black-box optimization in VAE latent space using decoder uncertainty](https://mlsanity.com/paper/2107.00096/) (2021)
- [Parallel Bayesian Global Optimization of Expensive Functions](https://mlsanity.com/paper/1602.05149/) (2016)
- [Uncertainty-Aware Search Framework for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2204.05944/) (2022)
- [Discovering Many Diverse Solutions with Bayesian Optimization](https://mlsanity.com/paper/2210.10953/) (2022)

## Abstract (arXiv)

In multi-objective black-box optimization, the goal is typically to find solutions that optimize a set of T black-box objective functions, f1, ldots fT, simultaneously. Traditional approaches often seek a single Pareto-optimal set that balances trade-offs among all objectives. In contrast, we consider a problem setting that departs from this paradigm: finding a small set of K < T solutions, that collectively "cover" the T objectives. A set of solutions is defined as "covering" if, for each objective f1, ldots fT, there is at least one good solution. A motivating example for this problem setting occurs in drug design. For example, we may have T pathogens and aim to identify a set of K < T antibiotics such that at least one antibiotic can be used to treat each pathogen. This problem, known as coverage optimization, has yet to be tackled with the Bayesian optimization (BO) framework. To fill this void, we develop Multi-Objective Coverage Bayesian Optimization (MOCOBO), a BO algorithm for solving coverage optimization. Our approach is based on a new acquisition function reminiscent of expected improvement in the vanilla BO setup. We demonstrate the performance of our method on high-dimensional black-box optimization tasks, including applications in peptide and molecular design. Results show that the coverage of the K < T solutions found by MOCOBO matches or nearly matches the coverage of T solutions obtained by optimizing each objective individually. Furthermore, in in vitro experiments, the peptides found by MOCOBO exhibited high potency against drug-resistant pathogens, further demonstrating the potential of MOCOBO for drug discovery. All of our code is publicly available at the following link: https://github.com/nataliemaus/mocobo.