# Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?

arXiv: https://arxiv.org/abs/2604.09417 · HTML: https://mlsanity.com/paper/2604.09417/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 66 of its 133 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 30 of 66)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [Practical Multi-fidelity Bayesian Optimization for Hyperparameter Tuning](https://mlsanity.com/paper/1903.04703/) (2019)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [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)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization](https://mlsanity.com/paper/2006.04655/) (2020)
- [Multi-objective Bayesian Optimization using Pareto-frontier Entropy](https://mlsanity.com/paper/1906.00127/) (2019)
- [A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1811.00755/) (2018)
- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [Benchmarking the Performance of Bayesian Optimization across Multiple Experimental Materials Science Domains](https://mlsanity.com/paper/2106.01309/) (2021)
- [GIBBON: General-purpose Information-Based Bayesian OptimisatioN](https://mlsanity.com/paper/2102.03324/) (2021)
- [Multi-Fidelity Bayesian Optimization via Deep Neural Networks](https://mlsanity.com/paper/2007.03117/) (2020)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Uncertainty-Aware Search Framework for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2204.05944/) (2022)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Are Random Decompositions all we need in High Dimensional Bayesian Optimisation?](https://mlsanity.com/paper/2301.12844/) (2023)

## Built on by (most cited first, 2 of 2)

- [When to Use Which? Benchmarking Optimisers for Configurable Systems under Varying Budgets](https://mlsanity.com/paper/2607.16476/) (2026)
- [Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation](https://mlsanity.com/paper/2609.13396/) (2026)

## Abstract (arXiv)

Many-objective optimisation, a subset of multi-objective optimisation, involves optimisation problems with more than three objectives. As the number of objectives increases, the number of solutions needed to adequately represent the entire Pareto front typically grows substantially. This makes it challenging, if not infeasible, to design a search algorithm capable of effectively exploring the entire Pareto front. This difficulty is particularly acute in the Bayesian optimisation paradigm, where sample efficiency is critical and only a limited number of solutions (often a few hundred) are evaluated. Moreover, after the optimisation process, the decision-maker eventually selects just one solution for deployment, regardless of how many high-quality, diverse solutions are available. In light of this, we argue an idea that under a very limited evaluation budget, it may be more useful to focus on finding a single solution of the highest possible quality for the decision-maker, rather than aiming to approximate the entire Pareto front as existing many-/multi-objective Bayesian optimisation methods typically do. Bearing this idea in mind, this paper proposes a underlinesingle underlinepoint-based underlinemulti-underlineobjective search framework (SPMO) that aims to improve the quality of solutions along a direction that leads to a good tradeoff between objectives. Within SPMO, we present a simple acquisition function, called expected single-point improvement (ESPI), working under both noiseless and noisy scenarios. We show that ESPI can be optimised effectively with gradient-based methods via the sample average approximation (SAA) approach and theoretically prove its convergence guarantees under the SAA. We also empirically demonstrate that the proposed SPMO is computationally tractable and outperforms state-of-the-arts on a wide range of benchmark and real-world problems.