Optimal simulation-based Bayesian decisions
Justin Alsing Thomas D. P. Edwards Benjamin Wandelt
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.