# Rectified Max-Value Entropy Search for Bayesian Optimization

arXiv: https://arxiv.org/abs/2202.13597 · HTML: https://mlsanity.com/paper/2202.13597/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 18 references that are in the map.
- First posted on arXiv 28 Feb 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [Multi-fidelity Bayesian Optimization with Max-value Entropy Search and its parallelization](https://mlsanity.com/paper/1901.08275/) (2019)
- [Fast Information-theoretic Bayesian Optimisation](https://mlsanity.com/paper/1711.00673/) (2017)

## Built on by (most cited first, 6 of 6)

- [Joint Entropy Search for Maximally-Informed Bayesian Optimization](https://mlsanity.com/paper/2206.04771/) (2022)
- [Self-Correcting Bayesian Optimization through Bayesian Active Learning](https://mlsanity.com/paper/2304.11005/) (2023)
- [Active Learning and Bayesian Optimization: a Unified Perspective to Learn with a Goal](https://mlsanity.com/paper/2303.01560/) (2023)
- [Information-theoretic Bayesian Optimization: Survey and Tutorial](https://mlsanity.com/paper/2502.06789/) (2025)
- [α-PFN: Fast Entropy Search via In-Context Learning](https://mlsanity.com/paper/2606.07134/) (2026)
- [Alpha Entropy Search for New Information-based Bayesian Optimization](https://mlsanity.com/paper/2411.16586/) (2024)

## Abstract (arXiv)

Although the existing max-value entropy search (MES) is based on the widely celebrated notion of mutual information, its empirical performance can suffer due to two misconceptions whose implications on the exploration-exploitation trade-off are investigated in this paper. These issues are essential in the development of future acquisition functions and the improvement of the existing ones as they encourage an accurate measure of the mutual information such as the rectified MES (RMES) acquisition function we develop in this work. Unlike the evaluation of MES, we derive a closed-form probability density for the observation conditioned on the max-value and employ stochastic gradient ascent with reparameterization to efficiently optimize RMES. As a result of a more principled acquisition function, RMES shows a consistent improvement over MES in several synthetic function benchmarks and real-world optimization problems.