Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs

TL;DR

This paper introduces an unbiased stochastic gradient-based optimization method using randomized MLMC for Bayesian experimental design, improving efficiency and accuracy in maximizing expected information gain.

Contribution

It develops an unbiased Monte Carlo estimator for the gradient of expected information gain, enabling more reliable stochastic optimization in Bayesian experimental design.

Findings

The proposed algorithm effectively optimizes experimental designs in test problems.

It performs well on realistic pharmacokinetic applications.

Unbiased estimator reduces bias in gradient estimation.

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.