Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs

Abstract

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 ${\ell }_2$-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.

arXiv commentmajor revision, 26 pages, 6 figures

References in corpus (11)

• Adam: A Method for Stochastic Optimization
• On the Convergence of Adam and Beyond
• Gradient-based stochastic optimization methods in Bayesian experimental design
• Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation
• Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain
• Variational Bayesian Optimal Experimental Design
• On Nesting Monte Carlo Estimators
• Decision-making under uncertainty: using MLMC for efficient estimation of EVPPI
• Multilevel Monte Carlo estimation of expected information gains
• A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments
• Multilevel Monte Carlo estimation of the expected value of sample information

Cited by in corpus (5)

• Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design
• Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance
• Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach
• Constructing unbiased gradient estimators with finite variance for conditional stochastic optimization
• Efficient Debiased Evidence Estimation by Multilevel Monte Carlo Sampling