Contextual Ranking and Selection with Gaussian Processes

TL;DR

This paper introduces a Gaussian process-based method for contextual ranking and selection, optimizing the identification of best alternatives across different contexts with high efficiency and low computational cost.

Contribution

It develops a novel GP-C-OCBA sampling policy for contextual ranking and selection, with proven optimal convergence rates and practical efficiency improvements.

Findings

The GP-C-OCBA policy achieves optimal convergence rates.

The method is computationally efficient and competitive in sampling.

It effectively models context-specific rewards using Gaussian processes.

Abstract

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.