# Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs

arXiv: https://arxiv.org/abs/2005.08414 · HTML: https://mlsanity.com/paper/2005.08414/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2020.

## Built on by (most cited first, 19 of 19)

- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [BED-LLM: Intelligent Information Gathering with LLMs and Bayesian Experimental Design](https://mlsanity.com/paper/2508.21184/) (2025)
- [Bayesian Experimental Design via Contrastive Diffusions](https://mlsanity.com/paper/2410.11826/) (2024)
- [Constructing unbiased gradient estimators with finite variance for conditional stochastic optimization](https://mlsanity.com/paper/2206.01991/) (2022)
- [On Estimating the Gradient of the Expected Information Gain in Bayesian Experimental Design](https://mlsanity.com/paper/2308.09888/) (2023)
- [Multilevel neural simulation-based inference](https://mlsanity.com/paper/2506.06087/) (2025)
- [Optimal randomized multilevel Monte Carlo for repeatedly nested expectations](https://mlsanity.com/paper/2301.04095/) (2023)
- [Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Need](https://mlsanity.com/paper/2402.02111/) (2024)
- [Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach](https://mlsanity.com/paper/2504.20319/) (2025)
- [Accelerated Learning on Large Scale Screens using Generative Library Models](https://mlsanity.com/paper/2510.16612/) (2025)
- [Evasion Attacks Against Bayesian Predictive Models](https://mlsanity.com/paper/2506.09640/) (2025)
- [Bayesian Experimental Design via Score Matching](https://mlsanity.com/paper/2607.08335/) (2026)
- [Sequential Bayesian experimental designs via reinforcement learning](https://mlsanity.com/paper/2202.07472/) (2022)
- [Leveraging Nested MLMC for Sequential Neural Posterior Estimation with Intractable Likelihoods](https://mlsanity.com/paper/2401.16776/) (2024)
- [Approximation of differential entropy in Bayesian optimal experimental design](https://mlsanity.com/paper/2510.00734/) (2025)
- [Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance](https://mlsanity.com/paper/2601.16425/) (2026)
- [Stochastic Dimension Zeroth-Order Estimator: Stable and Memory-Efficient Training of PINNs](https://mlsanity.com/paper/2603.24002/) (2026)
- [FairBED: A Bayesian Experimental Design Approach to Gathering Fairer Data](https://mlsanity.com/paper/2606.23515/) (2026)

## Abstract (arXiv)

In this paper we propose an efficient stochastic optimization algorithm to search for Bayesian experimental designs such that the expected information gain is maximized. The gradient of the expected information gain with respect to experimental design parameters is given by a nested expectation, for which the standard Monte Carlo method using a fixed number of inner samples yields a biased estimator. In this paper, applying the idea of randomized multilevel Monte Carlo (MLMC) methods, we introduce an unbiased Monte Carlo estimator for the gradient of the expected information gain with finite expected squared ℓ2-norm and finite expected computational cost per sample. Our unbiased estimator can be combined well with stochastic gradient descent algorithms, which results in our proposal of an optimization algorithm to search for an optimal Bayesian experimental design. Numerical experiments confirm that our proposed algorithm works well not only for a simple test problem but also for a more realistic pharmacokinetic problem.