# Respecting the limit:Bayesian optimization with a bound on the optimal value

arXiv: https://arxiv.org/abs/2411.04744 · HTML: https://mlsanity.com/paper/2411.04744/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 7 Nov 2024.

## Builds on (most cited first, 14 of 14)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [Greed is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation](https://mlsanity.com/paper/1911.12809/) (2019)
- [A Study of Bayesian Neural Network Surrogates for Bayesian Optimization](https://mlsanity.com/paper/2305.20028/) (2023)
- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature](https://mlsanity.com/paper/1411.0439/) (2014)
- [Knowing The What But Not The Where in Bayesian Optimization](https://mlsanity.com/paper/1905.02685/) (2019)
- [Fast Information-theoretic Bayesian Optimisation](https://mlsanity.com/paper/1711.00673/) (2017)
- [SnAKe: Bayesian Optimization with Pathwise Exploration](https://mlsanity.com/paper/2202.00060/) (2022)
- [Nonnegativity-Enforced Gaussian Process Regression](https://mlsanity.com/paper/2004.04632/) (2020)
- [Gaussian Process Sampling and Optimization with Approximate Upper and Lower Bounds](https://mlsanity.com/paper/2110.12087/) (2021)

## Abstract (arXiv)

In many real-world optimization problems, we have prior information about what objective function values are achievable. In this paper, we study the scenario that we have either exact knowledge of the minimum value or a, possibly inexact, lower bound on its value. We propose bound-aware Bayesian optimization (BABO), a Bayesian optimization method that uses a new surrogate model and acquisition function to utilize such prior information. We present SlogGP, a new surrogate model that incorporates bound information and adapts the Expected Improvement (EI) acquisition function accordingly. Empirical results on a variety of benchmarks demonstrate the benefit of taking prior information about the optimal value into account, and that the proposed approach significantly outperforms existing techniques. Furthermore, we notice that even in the absence of prior information on the bound, the proposed SlogGP surrogate model still performs better than the standard GP model in most cases, which we explain by its larger expressiveness.