Amortized Bayesian Decision Making for simulation-based models (2312.02674v2)

Abstract: Simulation-based inference (SBI) provides a powerful framework for inferring posterior distributions of stochastic simulators in a wide range of domains. In many settings, however, the posterior distribution is not the end goal itself -- rather, the derived parameter values and their uncertainties are used as a basis for deciding what actions to take. Unfortunately, because posterior distributions provided by SBI are (potentially crude) approximations of the true posterior, the resulting decisions can be suboptimal. Here, we address the question of how to perform Bayesian decision making on stochastic simulators, and how one can circumvent the need to compute an explicit approximation to the posterior. Our method trains a neural network on simulated data and can predict the expected cost given any data and action, and can, thus, be directly used to infer the action with lowest cost. We apply our method to several benchmark problems and demonstrate that it induces similar cost as the true posterior distribution. We then apply the method to infer optimal actions in a real-world simulator in the medical neurosciences, the Bayesian Virtual Epileptic Patient, and demonstrate that it allows to infer actions associated with low cost after few simulations.

• The paper introduces BAM, a novel method that bypasses full posterior estimation by directly predicting expected costs with a neural network.
• The paper demonstrates that BAM reduces computational costs by up to an order of magnitude on complex simulation tasks compared to traditional methods.
• The paper validates BAM’s practical utility through applications, such as optimizing intervention strategies in simulation models of neural activity related to epilepsy.

Simulation-based inference (SBI) is a growing area of research focusing on deriving insights from complex models that are analytically intractable and can only be understood through simulated data. While SBI techniques can provide a distribution of possible parameter values (posterior distributions), a critical task often involves using these inferred parameters to make decisions, especially when there are costs associated with the actions taken. However, the traditional process of inferring a posterior distribution and then estimating the action that minimizes cost can be inefficient and may not provide the best outcomes, particularly when the posterior approximation is not perfect.

To tackle these inefficiencies, this paper introduces a novel method called Bayesian Amortized decision Making (BAM), which eliminates the middle step of approximating the full posterior distribution. Instead, BAM uses a neural network to predict the expected costs of actions directly from data, and can drastically reduce computational requirements to milliseconds for each decision, even when computing the cost function is expensive.

The researchers tested the performance of BAM against a standard method—Neural Posterior Estimation Monte-Carlo (NPE-MC)—across a suite of benchmark tasks varying in complexity. They found that for simpler statistical tasks, both NPE-MC and BAM were effective and accurate. However, for more demanding tasks involving complex simulations like the SIR (susceptible-infected-removed) model and the Lotka-Volterra predator-prey dynamics, BAM significantly outperformed NPE-MC and reduced the computational cost, at times by an order of magnitude.

Furthermore, an application to a simulator of neural activity associated with epilepsy—the Bayesian Virtual Epileptic Patient (BVEP)—demonstrated the practical utility of both methods in a healthcare context. The decision-making task involved choosing appropriate interventions for brain regions based on their level of excitability, and both BAM and NPE-MC were able to arrive at optimal decisions with only a limited number of simulations.

In summary, BAM proves to be a powerful method for simulation-based decision making, especially for complex systems where obtaining an accurate posterior distribution is difficult or the cost function is computationally intense. This paper contributes to the repertoire of tools available for those dealing with decision-making under uncertainty in numerous domains, from public health to engineering. While BAM specifically tailors to individual decision-based tasks and forgoes the general posterior distribution, its efficiency benefits cannot be overlooked, particularly when specific actions are required in large and complex models.