# Generalizing Bayesian Optimization with Decision-theoretic Entropies

arXiv: https://arxiv.org/abs/2210.01383 · HTML: https://mlsanity.com/paper/2210.01383/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 64 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 17 of 17)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [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)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [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)
- [Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification](https://mlsanity.com/paper/2011.09588/) (2020)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [Uncertainty Toolbox: an Open-Source Library for Assessing, Visualizing, and Improving Uncertainty Quantification](https://mlsanity.com/paper/2109.10254/) (2021)
- [Interactive Weak Supervision: Learning Useful Heuristics for Data Labeling](https://mlsanity.com/paper/2012.06046/) (2020)
- [Cost-aware Bayesian Optimization](https://mlsanity.com/paper/2003.10870/) (2020)
- [Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information](https://mlsanity.com/paper/2104.09460/) (2021)
- [Multi-Step Budgeted Bayesian Optimization with Unknown Evaluation Costs](https://mlsanity.com/paper/2111.06537/) (2021)
- [Graph Neural Network Bandits](https://mlsanity.com/paper/2207.06456/) (2022)
- [Amortized Auto-Tuning: Cost-Efficient Bayesian Transfer Optimization for Hyperparameter Recommendation](https://mlsanity.com/paper/2106.09179/) (2021)

## Built on by (most cited first, 11 of 11)

- [Rethinking Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2412.20892/) (2024)
- [Amortized Bayesian Experimental Design for Decision-Making](https://mlsanity.com/paper/2411.02064/) (2024)
- [Robust Entropy Search for Safe Efficient Bayesian Optimization](https://mlsanity.com/paper/2405.19059/) (2024)
- [Mastering the exploration-exploitation trade-off in Bayesian Optimization](https://mlsanity.com/paper/2305.08624/) (2023)
- [Information-theoretic Bayesian Optimization: Survey and Tutorial](https://mlsanity.com/paper/2502.06789/) (2025)
- [Informed Initialization for Bayesian Optimization and Active Learning](https://mlsanity.com/paper/2510.23681/) (2025)
- [Loss-Driven Bayesian Active Learning](https://mlsanity.com/paper/2604.11995/) (2026)
- [Targeted active learning for probabilistic models](https://mlsanity.com/paper/2210.12122/) (2022)
- [Alpha Entropy Search for New Information-based Bayesian Optimization](https://mlsanity.com/paper/2411.16586/) (2024)
- [Ideal Abstractions for Decision-Focused Learning](https://mlsanity.com/paper/2303.17062/) (2023)
- [Neural Nonmyopic Bayesian Optimization in Dynamic Cost Settings](https://mlsanity.com/paper/2601.06505/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) is a popular method for efficiently inferring optima of an expensive black-box function via a sequence of queries. Existing information-theoretic BO procedures aim to make queries that most reduce the uncertainty about optima, where the uncertainty is captured by Shannon entropy. However, an optimal measure of uncertainty would, ideally, factor in how we intend to use the inferred quantity in some downstream procedure. In this paper, we instead consider a generalization of Shannon entropy from work in statistical decision theory (DeGroot 1962, Rao 1984), which contains a broad class of uncertainty measures parameterized by a problem-specific loss function corresponding to a downstream task. We first show that special cases of this entropy lead to popular acquisition functions used in BO procedures such as knowledge gradient, expected improvement, and entropy search. We then show how alternative choices for the loss yield a flexible family of acquisition functions that can be customized for use in novel optimization settings. Additionally, we develop gradient-based methods to efficiently optimize our proposed family of acquisition functions, and demonstrate strong empirical performance on a diverse set of sequential decision making tasks, including variants of top-k optimization, multi-level set estimation, and sequence search.