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

We present a framework for the efficient computation of optimal Bayesian
decisions under intractable likelihoods, by learning a surrogate model for the
expected utility (or its distribution) as a function of the action and data
spaces. We leverage recent advances in simulation-based inference and Bayesian
optimization to develop active learning schemes to choose where in parameter
and action spaces to simulate. This allows us to learn the optimal action in as
few simulations as possible. The resulting framework is extremely simulation
efficient, typically requiring fewer model calls than the associated posterior
inference task alone, and a factor of $100-1000$ more efficient than
Monte-Carlo based methods. Our framework opens up new capabilities for
performing Bayesian decision making, particularly in the previously challenging
regime where likelihoods are intractable, and simulations expensive.

通过学习预期效用（或其分布）作为动作和数据空间的函数的代理模型，我们提出了一个高效计算在难以计算的似然函数下的最优贝叶斯决策的框架。我们利用基于模拟的推断和贝叶斯优化的最新进展，开发了主动学习方案来选择参数和动作空间中要模拟的位置，从而尽可能少地进行模拟来学习最优动作。该框架非常高效，通常需要的模型调用次数比相关的后验推断任务少，并且比基于蒙特卡洛方法的方法高出 100-1000 倍。我们的框架为进行贝叶斯决策提供了新的能力，特别是在似然函数难以处理且模拟昂贵的挑战性领域。