# Constrained Bayesian Experimental Design via Online Planning

arXiv: https://arxiv.org/abs/2605.26990 · HTML: https://mlsanity.com/paper/2605.26990/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 77 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 30 of 44)

- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modeling](https://mlsanity.com/paper/2207.04179/) (2022)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [Prediction-Oriented Bayesian Active Learning](https://mlsanity.com/paper/2304.08151/) (2023)
- [Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods](https://mlsanity.com/paper/2111.02329/) (2021)
- [A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments](https://mlsanity.com/paper/1911.00294/) (2019)
- [Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimation](https://mlsanity.com/paper/2002.08129/) (2020)
- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Optimizing Sequential Experimental Design with Deep Reinforcement Learning](https://mlsanity.com/paper/2202.00821/) (2022)
- [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)
- [BINOCULARS for Efficient, Nonmyopic Sequential Experimental Design](https://mlsanity.com/paper/1909.04568/) (2019)
- [Efficient Bayesian Experimental Design for Implicit Models](https://mlsanity.com/paper/1810.09912/) (2018)
- [Sequential Bayesian optimal experimental design via approximate dynamic programming](https://mlsanity.com/paper/1604.08320/) (2016)
- [Sequential Bayesian Experimental Design for Implicit Models via Mutual Information](https://mlsanity.com/paper/2003.09379/) (2020)
- [Amortized Probabilistic Conditioning for Optimization, Simulation and Inference](https://mlsanity.com/paper/2410.15320/) (2024)
- [Amortized Bayesian Experimental Design for Decision-Making](https://mlsanity.com/paper/2411.02064/) (2024)
- [Efficient Rollout Strategies for Bayesian Optimization](https://mlsanity.com/paper/2002.10539/) (2020)
- [A Nonmyopic Approach to Cost-Constrained Bayesian Optimization](https://mlsanity.com/paper/2106.06079/) (2021)
- [HyP-DESPOT: A Hybrid Parallel Algorithm for Online Planning under Uncertainty](https://mlsanity.com/paper/1802.06215/) (2018)
- [Multi-Step Budgeted Bayesian Optimization with Unknown Evaluation Costs](https://mlsanity.com/paper/2111.06537/) (2021)
- [Policy-Based Bayesian Experimental Design for Non-Differentiable Implicit Models](https://mlsanity.com/paper/2203.04272/) (2022)
- [Cost-aware Bayesian Optimization via the Pandora's Box Gittins Index](https://mlsanity.com/paper/2406.20062/) (2024)
- [Safe Active Learning for Multi-Output Gaussian Processes](https://mlsanity.com/paper/2203.14849/) (2022)

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

- [Efficient Adaptive Data Acquisition via Pretrained Belief Representations](https://mlsanity.com/paper/2606.25197/) (2026)
- [Certifying Interventional Agreement Among Observationally Equivalent Causal Models](https://mlsanity.com/paper/2609.32247/) (2026)

## Abstract (arXiv)

Bayesian experimental design (BED) is a principled framework for data-efficient design of sequential experiments. However, existing BED methods are unable to adapt to dynamic constraints inherent in real-world tasks due to budget limitations, varying costs, or physical constraints that restrict how designs evolve over time. In this paper, we introduce a novel approach to BED that enables constrained optimization of experimental designs by combining offline pre-training of an amortized policy and a posterior network with online multi-step lookahead planning using scenario trees. We empirically demonstrate that our method yields substantially more informative design sequences than existing methods across a range of constrained BED tasks, while incurring only a modest additional computational overhead.