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Paper · 2005.08414 · 2020

Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs

arXiv · PDF · Open in the Atlas

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RepositoryRoleRan
Goda-Research-Group/MLMC_stochastic_gradient canonical 6 of 9
FunctionStatusWhere it lives
amsgrad_initialize Ran Goda-Research-Group/MLMC_stochastic_gradient/mlmc_eig_grad/optimize.py
code served (permissive licence) · get_code("0577addb049ea50b")
amsgrad_iterate Ran Goda-Research-Group/MLMC_stochastic_gradient/mlmc_eig_grad/optimize.py
code served (permissive licence) · get_code("1d6211e990fb0d6e")
dist_theta_pdf_test Ran Goda-Research-Group/MLMC_stochastic_gradient/mlmc_eig_grad/models.py
code served (permissive licence) · get_code("59d8f17f7362768b")
dist_theta_rvs_test Ran Goda-Research-Group/MLMC_stochastic_gradient/mlmc_eig_grad/models.py
code served (permissive licence) · get_code("54916a5656cc2b87")
dist_y_rvs_test Ran Goda-Research-Group/MLMC_stochastic_gradient/mlmc_eig_grad/models.py
code served (permissive licence) · get_code("466e0c7a63b5a8df")
robbins_monro_initialize Ran Goda-Research-Group/MLMC_stochastic_gradient/mlmc_eig_grad/optimize.py
code served (permissive licence) · get_code("06fdd30684b0e2b8")
mlmc_eig_grad Not yet run Goda-Research-Group/MLMC_stochastic_gradient/mlmc_eig_grad/mlmc_eig.py
code served (permissive licence) · get_code("18e16614cf3dfd83")
mlmc_eig_value Not yet run Goda-Research-Group/MLMC_stochastic_gradient/mlmc_eig_grad/mlmc_eig.py
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mlmc_eig_value_and_grad Not yet run Goda-Research-Group/MLMC_stochastic_gradient/mlmc_eig_grad/mlmc_eig.py
code served (permissive licence) · get_code("bdc22bb94134802b")

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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.

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