Validation of the α-selection strategy based on asymptotic inefficiency in MLMC for SNPE

Determine whether selecting the geometric level-distribution parameter α by minimizing asymptotic inefficiency (defined as the product of estimator variance and average computational cost) yields consistent improvement in training stability, convergence, and posterior approximation accuracy compared to the conventional choice that minimizes average cost, for the multi-level Monte Carlo estimators (RU-MLMC, GRR-MLMC, and TGRR-MLMC) used to estimate the nested Automatic Posterior Transformation (APT) loss and gradient in sequential neural posterior estimation with intractable likelihoods.

Background

The paper introduces a nested APT method for sequential neural posterior estimation (SNPE) and develops MLMC-based estimators (RU-MLMC, GRR-MLMC, and TGRR-MLMC) to address the bias/variance trade-offs inherent in nested estimation of the normalizing constant and its gradients. A key hyperparameter in these MLMC methods is α, the parameter of the geometric distribution controlling the random level selection and thus the balance between variance and cost.

While prior works typically choose α to minimize average computational cost, the authors propose instead to choose α to minimize asymptotic inefficiency (variance × cost), motivated by the observed dominance of variance in training dynamics. However, this proposed strategy lacks thorough empirical validation via ablation studies, leaving it uncertain whether it consistently improves performance across SNPE tasks.