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.

翻译：我们提出一个框架，用于在似然函数难以处理的情况下高效计算最优贝叶斯决策。该框架通过学习一个关于动作空间与数据空间的期望效用（或其分布）的代理模型实现。我们利用模拟推断与贝叶斯优化的最新进展，开发出主动学习方案，以选择在参数空间和动作空间中进行仿真的位置。这使得我们能够以最少的仿真次数学习最优动作。该框架在仿真效率上极其高效，通常所需的模型调用次数少于后验推理任务本身，且比基于蒙特卡洛的方法效率高出100到1000倍。我们的框架开辟了执行贝叶斯决策的新能力，尤其适用于似然函数难以处理且仿真成本高昂的此前具有挑战性的场景。