论文标题
公正的MLMC随机梯度基于贝叶斯实验设计的优化
Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs
论文作者
论文摘要
在本文中，我们提出了一种有效的随机优化算法来搜索贝叶斯实验设计，以便最大程度地提高预期信息增益。相对于实验设计参数的预期信息增益的梯度由嵌套期望给出，使用固定数量的内部样品的标准蒙特卡洛方法产生了偏置的估计器。在本文中，应用随机多级蒙特卡洛（MLMC）方法的想法，我们引入了一个无偏的蒙特卡洛估计器，以实现预期信息增益的梯度，并使用有限的预期平方$ \ ell_2 $ norm和有限的预期计算成本。我们的无偏估计器可以与随机梯度下降算法完美结合，这导致我们提出的优化算法以搜索最佳的贝叶斯实验设计。数值实验证实，我们提出的算法不仅在简单的测试问题上也很好地效果很好，而且对于更现实的药代动力学问题。
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.
