Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs
This work addresses the challenge of biased gradient estimation in Bayesian experimental design optimization, offering an incremental improvement for researchers in statistics and machine learning.
The paper tackles the problem of optimizing Bayesian experimental designs by maximizing expected information gain, proposing an unbiased stochastic gradient estimator using randomized multilevel Monte Carlo (MLMC) methods, and demonstrates its effectiveness in numerical experiments including a pharmacokinetic problem.
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.