# Contextual Ranking and Selection with Gaussian Processes

arXiv: https://arxiv.org/abs/2201.07782 · HTML: https://mlsanity.com/paper/2201.07782/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2022.

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

In many real world problems, we are faced with the problem of selecting the best among a finite number of alternatives, where the best alternative is determined based on context specific information. In this work, we study the contextual Ranking and Selection problem under a finite-alternative-finite-context setting, where we aim to find the best alternative for each context. We use a separate Gaussian process to model the reward for each alternative, and derive the large deviations rate function for both the expected and worst-case contextual probability of correct selection. We propose the GP-C-OCBA sampling policy, which uses the Gaussian process posterior to iteratively allocate observations to maximize the rate function. We prove its consistency and show that it achieves the optimal convergence rate under the assumption of a non-informative prior. Numerical experiments show that our algorithm is highly competitive in terms of sampling efficiency, while having significantly smaller computational overhead.