# Bayesian Optimization of Function Networks with Partial Evaluations

arXiv: https://arxiv.org/abs/2311.02146 · HTML: https://mlsanity.com/paper/2311.02146/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 3 Nov 2023.

## Builds on (most cited first, 25 of 25)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Multi-Goal Reinforcement Learning: Challenging Robotics Environments and Request for Research](https://mlsanity.com/paper/1802.09464/) (2018)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Practical Multi-fidelity Bayesian Optimization for Hyperparameter Tuning](https://mlsanity.com/paper/1903.04703/) (2019)
- [A Literature Survey of Benchmark Functions For Global Optimization Problems](https://mlsanity.com/paper/1308.4008/) (2013)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables](https://mlsanity.com/paper/1910.01688/) (2019)
- [A General Framework for Constrained Bayesian Optimization using Information-based Search](https://mlsanity.com/paper/1511.09422/) (2015)
- [Bayesian Optimization of Composite Functions](https://mlsanity.com/paper/1906.01537/) (2019)
- [Cost-aware Bayesian Optimization](https://mlsanity.com/paper/2003.10870/) (2020)
- [Efficient Nonmyopic Bayesian Optimization via One-Shot Multi-Step Trees](https://mlsanity.com/paper/2006.15779/) (2020)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Bayesian Optimization of Function Networks](https://mlsanity.com/paper/2112.15311/) (2021)
- [Thinking inside the box: A tutorial on grey-box Bayesian optimization](https://mlsanity.com/paper/2201.00272/) (2022)
- [Production Machine Learning Pipelines: Empirical Analysis and Optimization Opportunities](https://mlsanity.com/paper/2103.16007/) (2021)
- [A Nonmyopic Approach to Cost-Constrained Bayesian Optimization](https://mlsanity.com/paper/2106.06079/) (2021)
- [Multi-Step Budgeted Bayesian Optimization with Unknown Evaluation Costs](https://mlsanity.com/paper/2111.06537/) (2021)
- [Bayesian Optimization for Cascade-type Multi-stage Processes](https://mlsanity.com/paper/2111.08330/) (2021)
- [Bayesian optimization for modular black-box systems with switching costs](https://mlsanity.com/paper/2006.02624/) (2020)
- [Knowledge Gradient for Multi-Objective Bayesian Optimization with Decoupled Evaluations](https://mlsanity.com/paper/2302.01310/) (2023)
- [Efficient computation of the Knowledge Gradient for Bayesian Optimization](https://mlsanity.com/paper/2209.15367/) (2022)
- [Bayesian Optimization for Function Compositions with Applications to Dynamic Pricing](https://mlsanity.com/paper/2303.11954/) (2023)

## Built on by (most cited first, 10 of 10)

- [BONSAI: Structure-exploiting robust Bayesian optimization for networked black-box systems under uncertainty](https://mlsanity.com/paper/2510.03893/) (2025)
- [No-Regret Learning of Nash Equilibrium for Black-Box Games via Gaussian Processes](https://mlsanity.com/paper/2405.08318/) (2024)
- [Multi-Objective Bayesian Optimization for Networked Black-Box Systems: A Path to Greener Profits and Smarter Designs](https://mlsanity.com/paper/2502.14121/) (2025)
- [Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems](https://mlsanity.com/paper/2408.17387/) (2024)
- [NeuroPareto: Calibrated Acquisition for Costly Many-Goal Search in Vast Parameter Spaces](https://mlsanity.com/paper/2602.03901/) (2026)
- [Fast Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2506.11456/) (2025)
- [LLM-Driven Composite Neural Architecture Search for Multi-Source RL State Encoding](https://mlsanity.com/paper/2512.06982/) (2025)
- [Maximizing Reliability with Bayesian Optimization](https://mlsanity.com/paper/2602.02432/) (2026)
- [Bayesian Optimization of Partially Known Systems using Hybrid Models](https://mlsanity.com/paper/2603.11199/) (2026)
- [Exploiting Separability in Multi-Scale Grey-Box Bayesian Optimization](https://mlsanity.com/paper/2608.03045/) (2026)

## Abstract (arXiv)

Bayesian optimization is a powerful framework for optimizing functions that are expensive or time-consuming to evaluate. Recent work has considered Bayesian optimization of function networks (BOFN), where the objective function is given by a network of functions, each taking as input the output of previous nodes in the network as well as additional parameters. Leveraging this network structure has been shown to yield significant performance improvements. Existing BOFN algorithms for general-purpose networks evaluate the full network at each iteration. However, many real-world applications allow for evaluating nodes individually. To exploit this, we propose a novel knowledge gradient acquisition function that chooses which node and corresponding inputs to evaluate in a cost-aware manner, thereby reducing query costs by evaluating only on a part of the network at each step. We provide an efficient approach to optimizing our acquisition function and show that it outperforms existing BOFN methods and other benchmarks across several synthetic and real-world problems. Our acquisition function is the first to enable cost-aware optimization of a broad class of function networks.