# Ranking and Selection as Stochastic Control

arXiv: https://arxiv.org/abs/1710.02619 · HTML: https://mlsanity.com/paper/1710.02619/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2017.

## Built on by (most cited first, 9 of 9)

- [Welfare Maximization Algorithm for Solving Budget-Constrained Multi-Component POMDPs](https://mlsanity.com/paper/2303.10302/) (2023)
- [Combined Global and Local Search for Optimization with Gaussian Process Models](https://mlsanity.com/paper/2107.03217/) (2021)
- [An Efficient Dynamic Sampling Policy For Monte Carlo Tree Search](https://mlsanity.com/paper/2204.12043/) (2022)
- [An Actor-Critic Method for Simulation-Based Optimization](https://mlsanity.com/paper/2111.00435/) (2021)
- [Selection of the Most Probable Best](https://mlsanity.com/paper/2207.07533/) (2022)
- [Asymptotic Optimality of Myopic Ranking and Selection Procedures](https://mlsanity.com/paper/2211.14723/) (2022)
- [Efficient Learning for Selecting Top-m Context-Dependent Designs](https://mlsanity.com/paper/2305.04086/) (2023)
- [Series Expansion of Probability of Correct Selection for Improved Finite Budget Allocation in Ranking and Selection](https://mlsanity.com/paper/2411.10695/) (2024)
- [Sequential Additivity in Distributionally Robust Ranking and Selection](https://mlsanity.com/paper/2509.06147/) (2025)

## Abstract (arXiv)

Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function approximation, we derive an approximately optimal allocation policy. We show that this policy is not only computationally efficient but also possesses both one-step-ahead and asymptotic optimality for independent normal sampling distributions. Moreover, the proposed allocation policy is easily generalizable in the approximate dynamic programming paradigm.