Optimal simulation-based Bayesian decisions

TL;DR

This paper introduces a simulation-efficient framework for computing optimal Bayesian decisions with intractable likelihoods by learning surrogate models and using active learning to minimize simulations.

Contribution

It develops a novel active learning approach leveraging Bayesian optimization to efficiently identify optimal actions with fewer simulations than traditional methods.

Findings

Requires 100-1000 times fewer simulations than Monte Carlo methods

Achieves high efficiency in intractable likelihood scenarios

Enables Bayesian decision making with expensive simulations

Abstract

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.