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.

该研究利用基于仿真的推断方法解决了如何在随机模拟器上进行贝叶斯决策，并且通过训练神经网络预测期望成本，以推断具有最低成本的行动。

基于摊还的贝叶斯决策模拟建模

Amortized Bayesian Decision Making for simulation-based models

Recent work has discussed the limitations of counterfactual explanations to
recommend actions for algorithmic recourse, and argued for the need of taking
causal relationships between features into consideration. Unfortunately, in
practice, the true underlying structural causal model is generally unknown. In
this work, we first show that it is impossible to guarantee recourse without
access to the true structural equations. To address this limitation, we propose
two probabilistic approaches to select optimal actions that achieve recourse
with high probability given limited causal knowledge (e.g., only the causal
graph). The first captures uncertainty over structural equations under additive
Gaussian noise, and uses Bayesian model averaging to estimate the
counterfactual distribution. The second removes any assumptions on the
structural equations by instead computing the average effect of recourse
actions on individuals similar to the person who seeks recourse, leading to a
novel subpopulation-based interventional notion of recourse. We then derive a
gradient-based procedure for selecting optimal recourse actions, and
empirically show that the proposed approaches lead to more reliable
recommendations under imperfect causal knowledge than non-probabilistic
baselines.

通过两种概率方法选取最优行动以在有限的因果知识下实现补救，以解决缺乏真实结构因果模型的限制，并在不完美的因果知识下提供比非概率基线更可靠的建议。