# Asymptotically Optimal Sampling Policy for Selecting Top-m Alternatives

arXiv: https://arxiv.org/abs/2111.15172 · HTML: https://mlsanity.com/paper/2111.15172/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2021.

## Built on by (most cited first, 3 of 3)

- [Information-Directed Selection for Top-Two Algorithms](https://mlsanity.com/paper/2205.12086/) (2022)
- [Selecting the Best Optimizing System](https://mlsanity.com/paper/2201.03065/) (2022)
- [Efficient Learning for Selecting Top-m Context-Dependent Designs](https://mlsanity.com/paper/2305.04086/) (2023)

## Abstract (arXiv)

We consider selecting the top-m alternatives from a finite number of alternatives via Monte Carlo simulation. Under a Bayesian framework, we formulate the sampling decision as a stochastic dynamic programming problem, and develop a sequential sampling policy that maximizes a value function approximation one-step look ahead. To show the asymptotic optimality of the proposed procedure, the asymptotically optimal sampling ratios which optimize large deviations rate of the probability of false selection for selecting top-m alternatives has been rigorously defined. The proposed sampling policy is not only proved to be consistent but also achieves the asymptotically optimal sampling ratios. Numerical experiments demonstrate superiority of the proposed allocation procedure over existing ones.