Alternative Strategies for Active Learning with Bayesian Bradley Terry Model
Abstract
Comparative judgement uses pairwise comparisons to rank items, but recovering accurate rankings from a limited number of judgements depends on both the inference method and the pairs selected. We developed a Bayesian Bradley-Terry model (BBTM) that uses Polya-Gamma data augmentation for efficient Gibbs sampling and quantifies uncertainty in latent abilities and ranks. We propose three active learning strategies based on the knowledge gradient (KG) principle. We define our acquisition functions using Kendall's tau distance, posterior rank entropy, and posterior separation. Approximate one-step updates to posterior moments reduce the computational cost of evaluating candidate pairs. We also introduce Posterior Separation Reliability (PSR), which measures the spread of posterior mean abilities relative to posterior uncertainty. It provides an internal indicator of ranking reliability without requiring a reference ranking. In synthetic experiments covering different item counts, comparison budgets, and noise levels, BBTM generally recovers ranking more accurately than preference-based Bayesian comparative judgement (PBCJ). At low to moderate noise levels, the pairwise entropy pair selection strategy performs best in ranking recovery. However, at the highest noise levels, the KG strategy based on posterior separation produces better point rankings. PSR increases alongside improvements in ranking accuracy as comparisons accumulate. Robustness experiments identify the proportion of informative outcomes needed to meet specified accuracy targets within a fixed comparison budget. In a moderate noise setting, replacing 30\% of outcomes with random choices has little effect on ranking performance. These findings demonstrate the value of Bayesian inference and active learning pair selection for recovering ranks from limited, noisy paired comparisons.
Related
- Active learning confidence measures for coupling strategies in digital twins integrating simulation and data-driven submodels
- Active learning strategies for the estimation of a feasible set defined from a vector output black-box simulator
- Compressed Active Subspaces for Scalable Bayesian Inference
- The Siemons--Wagner property and Bradley's conjecture
- Borwein-Bradley-type identities for Ramanujan-type series for 1/π4
BibTeX
@misc{jayasinghe2026alternative,
title = {{Alternative Strategies for Active Learning with Bayesian Bradley Terry Model}},
author = {Saman Jayasinghe and Sean Walton and Alma Rahat and Andy Gray and Chris Wheadon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29416},
eprint = {2610.29416},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29416},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Alternative Strategies for Active Learning with Bayesian Bradley Terry Model
AU - Saman Jayasinghe
AU - Sean Walton
AU - Alma Rahat
AU - Andy Gray
AU - Chris Wheadon
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29416
UR - https://arxiv.org/abs/2610.29416
AB - Comparative judgement uses pairwise comparisons to rank items, but recovering accurate rankings from a limited number of judgements depends on both the inference method and the pairs selected. We developed a Bayesian Bradley-Terry model (BBTM) that uses Polya-Gamma data augmentation for efficient Gibbs sampling and quantifies uncertainty in latent abilities and ranks. We propose three active learning strategies based on the knowledge gradient (KG) principle. We define our acquisition functions using Kendall's tau distance, posterior rank entropy, and posterior separation. Approximate one-step updates to posterior moments reduce the computational cost of evaluating candidate pairs. We also introduce Posterior Separation Reliability (PSR), which measures the spread of posterior mean abilities relative to posterior uncertainty. It provides an internal indicator of ranking reliability without requiring a reference ranking. In synthetic experiments covering different item counts, comparison budgets, and noise levels, BBTM generally recovers ranking more accurately than preference-based Bayesian comparative judgement (PBCJ). At low to moderate noise levels, the pairwise entropy pair selection strategy performs best in ranking recovery. However, at the highest noise levels, the KG strategy based on posterior separation produces better point rankings. PSR increases alongside improvements in ranking accuracy as comparisons accumulate. Robustness experiments identify the proportion of informative outcomes needed to meet specified accuracy targets within a fixed comparison budget. In a moderate noise setting, replacing 30\% of outcomes with random choices has little effect on ranking performance. These findings demonstrate the value of Bayesian inference and active learning pair selection for recovering ranks from limited, noisy paired comparisons.
ER -