# Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization

arXiv: https://arxiv.org/abs/2110.06980 · HTML: https://mlsanity.com/paper/2110.06980/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 71 references that are in the map.
- First posted on arXiv 13 Oct 2021.

## Builds on (most cited first, 25 of 25)

- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets](https://mlsanity.com/paper/1605.07079/) (2016)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1511.05467/) (2015)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [Combinatorial Bayesian Optimization using the Graph Cartesian Product](https://mlsanity.com/paper/1902.00448/) (2019)
- [BOCK : Bayesian Optimization with Cylindrical Kernels](https://mlsanity.com/paper/1806.01619/) (2018)
- [A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1811.00755/) (2018)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/1609.01051/) (2016)
- [Mercer Features for Efficient Combinatorial Bayesian Optimization](https://mlsanity.com/paper/2012.07762/) (2020)
- [A Bayesian approach to constrained single- and multi-objective optimization](https://mlsanity.com/paper/1510.00503/) (2015)
- [Bayesian Optimization over Hybrid Spaces](https://mlsanity.com/paper/2106.04682/) (2021)
- [Multi-Fidelity Multi-Objective Bayesian Optimization: An Output Space Entropy Search Approach](https://mlsanity.com/paper/2011.01542/) (2020)
- [Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction](https://mlsanity.com/paper/1310.0732/) (2013)
- [MUMBO: MUlti-task Max-value Bayesian Optimization](https://mlsanity.com/paper/2006.12093/) (2020)
- [Multi-fidelity Bayesian Optimization with Max-value Entropy Search and its parallelization](https://mlsanity.com/paper/1901.08275/) (2019)
- [Optimization as Estimation with Gaussian Processes in Bandit Settings](https://mlsanity.com/paper/1510.06423/) (2015)
- [Improved Max-value Entropy Search for Multi-objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2011.01150/) (2020)
- [Optimizing Discrete Spaces via Expensive Evaluations: A Learning to Search Framework](https://mlsanity.com/paper/2012.07320/) (2020)
- [Adaptive Rate of Convergence of Thompson Sampling for Gaussian Process Optimization](https://mlsanity.com/paper/1705.06808/) (2017)
- [Learning-based Application-Agnostic 3D NoC Design for Heterogeneous Manycore Systems](https://mlsanity.com/paper/1810.08869/) (2018)
- [Practical Bayesian Optimization for Variable Cost Objectives](https://mlsanity.com/paper/1703.04335/) (2017)
- [Design-Space Exploration and Optimization of an Energy-Efficient and Reliable 3D Small-world Network-on-Chip](https://mlsanity.com/paper/1608.06972/) (2016)
- [On-Chip Communication Network for Efficient Training of Deep Convolutional Networks on Heterogeneous Manycore Systems](https://mlsanity.com/paper/1712.02293/) (2017)

## Built on by (most cited first, 13 of 13)

- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Preference-Guided Diffusion for Multi-Objective Offline Optimization](https://mlsanity.com/paper/2503.17299/) (2025)
- [BOFormer: Learning to Solve Multi-Objective Bayesian Optimization via Non-Markovian RL](https://mlsanity.com/paper/2505.21974/) (2025)
- [In-Context Multi-Objective Optimization](https://mlsanity.com/paper/2512.11114/) (2025)
- [PF2ES: Parallel Feasible Pareto Frontier Entropy Search for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2204.05411/) (2022)
- [AReUReDi: Annealed Rectified Updates for Refining Discrete Flows with Multi-Objective Guidance](https://mlsanity.com/paper/2510.00352/) (2025)
- [Preference-Aware Constrained Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2303.13034/) (2023)
- [Information-theoretic Bayesian Optimization: Survey and Tutorial](https://mlsanity.com/paper/2502.06789/) (2025)
- [Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2604.09417/) (2026)
- [Swine Diet Design using Multi-objective Regionalized Bayesian Optimization](https://mlsanity.com/paper/2409.12919/) (2024)
- [Non-Myopic Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2412.08085/) (2024)
- [Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation](https://mlsanity.com/paper/2609.13396/) (2026)
- [pCoMole: Pareto-Constrained Molecule Editing with Discrete Flows](https://mlsanity.com/paper/2610.01663/) (2026)

## Abstract (arXiv)

We consider the problem of black-box multi-objective optimization (MOO) using expensive function evaluations (also referred to as experiments), where the goal is to approximate the true Pareto set of solutions by minimizing the total resource cost of experiments. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive computational simulations. The key challenge is to select the sequence of experiments to uncover high-quality solutions using minimal resources. In this paper, we propose a general framework for solving MOO problems based on the principle of output space entropy (OSE) search: select the experiment that maximizes the information gained per unit resource cost about the true Pareto front. We appropriately instantiate the principle of OSE search to derive efficient algorithms for the following four MOO problem settings: 1) The most basic em single-fidelity setting, where experiments are expensive and accurate; 2) Handling em black-box constraints} which cannot be evaluated without performing experiments; 3) The discrete multi-fidelity setting, where experiments can vary in the amount of resources consumed and their evaluation accuracy; and 4) The em continuous-fidelity setting, where continuous function approximations result in a huge space of experiments. Experiments on diverse synthetic and real-world benchmarks show that our OSE search based algorithms improve over state-of-the-art methods in terms of both computational-efficiency and accuracy of MOO solutions.