# Knowledge Gradient for Selection with Covariates: Consistency and Computation

arXiv: https://arxiv.org/abs/1906.05098 · HTML: https://mlsanity.com/paper/1906.05098/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2019.

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

- [Collaborative Bayesian Optimization via Wasserstein Barycenters](https://mlsanity.com/paper/2504.10770/) (2025)
- [On the Finite-Time Performance of the Knowledge Gradient Algorithm](https://mlsanity.com/paper/2206.06847/) (2022)
- [Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems](https://mlsanity.com/paper/2408.17387/) (2024)
- [Efficient Learning for Selecting Top-m Context-Dependent Designs](https://mlsanity.com/paper/2305.04086/) (2023)

## Abstract (arXiv)

Knowledge gradient is a design principle for developing Bayesian sequential sampling policies to solve optimization problems. In this paper we consider the ranking and selection problem in the presence of covariates, where the best alternative is not universal but depends on the covariates. In this context, we prove that under minimal assumptions, the sampling policy based on knowledge gradient is consistent, in the sense that following the policy the best alternative as a function of the covariates will be identified almost surely as the number of samples grows. We also propose a stochastic gradient ascent algorithm for computing the sampling policy and demonstrate its performance via numerical experiments.