Optimizing Likelihoods via Mutual Information: Bridging Simulation-Based Inference and Bayesian Optimal Experimental Design

摘要

Simulation-based inference (SBI) depends on expensive simulators, so inference and experimental design must operate under fixed simulation budgets. Bayesian optimal experimental design (BOED) maximizes expected information gain (EIG), but is often implemented with a separate mutual-information critic, used only as a diagnostic, or restricted to differentiable simulators. We show that the InfoNCE lower bound on EIG becomes a principled SBI training objective when the critic is a normalized conditional density model. Maximizing the bound is equivalent to fitting a surrogate likelihood by minimizing a KL divergence plus a marginal-likelihood term, so each simulator call can improve both inference and design. We propose SBI-BOED, a single stochastic-gradient procedure that jointly trains a conditional normalizing-flow likelihood and optimizes designs without simulator differentiability. The same MI view also yields simulation active learning under fixed designs via epistemic predictive information gain (EPIG). With an InfoNCE-λ objective and practical stabilizers, SBI-BOED improves posterior calibration and predictive accuracy over strong BOED baselines on synthetic benchmarks and scientific simulators at matched simulation budgets.