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.

翻译：仿真推断（SBI）为跨领域随机模拟器的后验分布推断提供了强大框架。然而在许多场景中，后验分布本身并非最终目标——而是将推导出的参数值及其不确定性作为决策依据。遗憾的是，由于SBI提供的后验分布仅是真实后验的（可能较为粗糙的）近似，据此做出的决策可能非最优。本文探讨如何在随机模拟器上执行贝叶斯决策，以及如何规避显式计算后验近似的问题。我们提出的方法在模拟数据上训练神经网络，能够根据任意数据和行动预测期望成本，从而直接推断成本最低的行动。在多个基准问题上的应用表明，该方法产生的成本与真实后验分布相近。进一步，我们将该方法应用于医学神经科学领域的真实模拟器——贝叶斯虚拟癫痫患者模型，验证了仅需少量仿真即可推断低关联成本的行动。