# A Parallel Technique for Multi-objective Bayesian Global Optimization: Using a Batch Selection of Probability of Improvement

arXiv: https://arxiv.org/abs/2208.03685 · HTML: https://mlsanity.com/paper/2208.03685/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 67 references that are in the map.
- First posted on arXiv 7 Aug 2022.

## Builds on (most cited first, 6 of 6)

- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1706.03673/) (2017)
- [Greed is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation](https://mlsanity.com/paper/1911.12809/) (2019)
- [Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithms](https://mlsanity.com/paper/1904.12672/) (2019)
- [Targeting Solutions in Bayesian Multi-Objective Optimization: Sequential and Batch Versions](https://mlsanity.com/paper/1811.03862/) (2018)
- [Asynchronous ε-Greedy Bayesian Optimisation](https://mlsanity.com/paper/2010.07615/) (2020)

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

- [A Trajectory-Based Bayesian Approach to Multi-Objective Hyperparameter Optimization with Epoch-Aware Trade-Offs](https://mlsanity.com/paper/2405.15303/) (2024)
- [Training Greedy Policy for Proposal Batch Selection in Expensive Multi-Objective Combinatorial Optimization](https://mlsanity.com/paper/2406.14876/) (2024)

## Abstract (arXiv)

Bayesian global optimization (BGO) is an efficient surrogate-assisted technique for problems involving expensive evaluations. A parallel technique can be used to parallelly evaluate the true-expensive objective functions in one iteration to boost the execution time. An effective and straightforward approach is to design an acquisition function that can evaluate the performance of a bath of multiple solutions, instead of a single point/solution, in one iteration. This paper proposes five alternatives of Probability of Improvement (PoI) with multiple points in a batch (q-PoI) for multi-objective Bayesian global optimization (MOBGO), taking the covariance among multiple points into account. Both exact computational formulas and the Monte Carlo approximation algorithms for all proposed q-PoIs are provided. Based on the distribution of the multiple points relevant to the Pareto-front, the position-dependent behavior of the five q-PoIs is investigated. Moreover, the five q-PoIs are compared with the other nine state-of-the-art and recently proposed batch MOBGO algorithms on twenty bio-objective benchmarks. The empirical experiments on different variety of benchmarks are conducted to demonstrate the effectiveness of two greedy q-PoIs (kpoi_mboxbest and kpoi_mboxall) on low-dimensional problems and the effectiveness of two explorative q-PoIs (kpoi_mboxone and kpoi_mboxworst) on high-dimensional problems with difficult-to-approximate Pareto front boundaries.