# Optimality in importance sampling: a gentle survey

arXiv: https://arxiv.org/abs/2502.07396 · HTML: https://mlsanity.com/paper/2502.07396/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2025.

## Built on by (most cited first, 4 of 4)

- [Effective sample size approximations as entropy measures](https://mlsanity.com/paper/2602.22954/) (2026)
- [From Minimax Optimal Importance Sampling to Uniformly Ergodic Importance-tempered MCMC](https://mlsanity.com/paper/2506.19186/) (2025)
- [Partition Function Estimation under Bounded f-Divergence](https://mlsanity.com/paper/2602.23535/) (2026)
- [A unifying view of contrastive learning, importance sampling, and bridge sampling for energy-based models](https://mlsanity.com/paper/2604.08116/) (2026)

## Abstract (arXiv)

The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This work is an exhaustive review around the concept of optimality in importance sampling. Several frameworks are described and analyzed, such as the marginal likelihood approximation for model selection, the use of multiple proposal densities, a sequence of tempered posteriors, and noisy scenarios including the applications to approximate Bayesian computation (ABC) and reinforcement learning, to name a few. Some theoretical and empirical comparisons are also provided.