A1510
Title: A Laplace-based policy approach to sequential Bayesian design
Authors: Emma Rowlinson - University of Manchester (United Kingdom) [presenting]
Tim Waite - University of Manchester (United Kingdom)
Abstract: Policy-based approaches have recently developed the ability to perform sequential Bayesian designs. These approaches involve the construction of a parametric function, called the policy, mapping from the current state of knowledge to a proposed design for the next experimental run. Policy-based approaches are inherently non-myopic, formulating the policy to optimize the total expected utility over the whole sequential experiment. Optimization of the policy is achieved via stochastic gradients, which are implemented using automatic differentiation. To parametrize the policy, i.e. represent the current state of knowledge, the use of a Laplace approximation to the posterior is proposed as a compact and computationally cheap way of capturing the information amassed after each experiment. As is typical, a neural network is chosen as the policy architecture, which is trained and then can be used to inform design decisions. Initial findings when considering a linear-Gaussian example suggest the method outperforms other approaches, providing closer to optimal designs. The rationale of a Laplace parametrization is discussed, and methodology for training policies for models is developed with both continuous and discrete responses, where the latter is more challenging due to the lack of differentiability of discrete random variable simulations. The performance of the method is demonstrated through examples.
