Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs
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.
Code (1)
Tasks
Experimental DesignStochastic OptimizationSimilar Papers 제목 키워드 기반
Efficient Debiased Evidence Estimation by Multilevel Monte Carlo Sampling
In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often use…
Bayesian InferenceStochastic OptimizationMulti-level Monte-Carlo Gradient Methods for Stochastic Optimization with Biased Oracles
We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures v…
Contrastive LearningSchedulingStochastic OptimizationOn the Bias-Variance-Cost Tradeoff of Stochastic Optimization
We consider stochastic optimization when one only has access to biased stochastic oracles of the objective, and obtaining stochastic gradients with low biases comes at high costs. This setting captures a variety of optim…
Bilevel OptimizationStochastic OptimizationOn the Parallel Complexity of Multilevel Monte Carlo in Stochastic Gradient Descent
In the stochastic gradient descent (SGD) for sequential simulations such as the neural stochastic differential equations, the Multilevel Monte Carlo (MLMC) method is known to offer better theoretical computational comple…
Smoothed Gradients for Stochastic Variational Inference
Stochastic variational inference (SVI) lets us scale up Bayesian computation to massive data. It uses stochastic optimization to fit a variational distribution, following easy-to-compute noisy natural gradients. As with …
Stochastic OptimizationVariational Inference