# Efficient Learning for Selecting Top-m Context-Dependent Designs

arXiv: https://arxiv.org/abs/2305.04086 · HTML: https://mlsanity.com/paper/2305.04086/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 63 references that are in the map.
- First posted on arXiv 6 May 2023.

## Builds on (most cited first, 15 of 15)

- [Contextual Bandits with Continuous Actions: Smoothing, Zooming, and Adapting](https://mlsanity.com/paper/1902.01520/) (2019)
- [Nearly Instance Optimal Sample Complexity Bounds for Top-k Arm Selection](https://mlsanity.com/paper/1702.03605/) (2017)
- [Review on Ranking and Selection: A New Perspective](https://mlsanity.com/paper/2008.00249/) (2020)
- [A Neural Networks Committee for the Contextual Bandit Problem](https://mlsanity.com/paper/1409.8191/) (2014)
- [Random Forest for the Contextual Bandit Problem - extended version](https://mlsanity.com/paper/1504.06952/) (2015)
- [Top-m identification for linear bandits](https://mlsanity.com/paper/2103.10070/) (2021)
- [Ranking and Selection with Covariates for Personalized Decision Making](https://mlsanity.com/paper/1710.02642/) (2017)
- [Ranking and Selection as Stochastic Control](https://mlsanity.com/paper/1710.02619/) (2017)
- [Sensitivity to Serial Dependency of Input Processes: A Robust Approach](https://mlsanity.com/paper/1606.06645/) (2016)
- [Distributionally Robust Selection of the Best](https://mlsanity.com/paper/1903.05828/) (2019)
- [Knowledge Gradient for Selection with Covariates: Consistency and Computation](https://mlsanity.com/paper/1906.05098/) (2019)
- [Efficient Learning for Clustering and Optimizing Context-Dependent Designs](https://mlsanity.com/paper/2012.05591/) (2020)
- [Asymptotically Optimal Sampling Policy for Selecting Top-m Alternatives](https://mlsanity.com/paper/2111.15172/) (2021)
- [Contextual Ranking and Selection with Gaussian Processes](https://mlsanity.com/paper/2201.07782/) (2022)
- [Sequential Design for Ranking Response Surfaces](https://mlsanity.com/paper/1509.00980/) (2015)

## Abstract (arXiv)

We consider a simulation optimization problem for a context-dependent decision-making, which aims to determine the top-m designs for all contexts. Under a Bayesian framework, we formulate the optimal dynamic sampling decision as a stochastic dynamic programming problem, and develop a sequential sampling policy to efficiently learn the performance of each design under each context. The asymptotically optimal sampling ratios are derived to attain the optimal large deviations rate of the worst-case of probability of false selection. The proposed sampling policy is proved to be consistent and its asymptotic sampling ratios are asymptotically optimal. Numerical experiments demonstrate that the proposed method improves the efficiency for selection of top-m context-dependent designs.