Boosting the Learning for Ranking Patterns

Pairwise Ranking Prompting (PRP) elicits pairwise preference judgments from an LLM, which are then aggregated into a ranking, usually via classical sorting algorithms. However, judgments are noisy, order-sensitive, and sometimes intransitive, so sorting assumptions do not match the setting. Because sorting aims to recover a full permutation, truncating it to meet a call budget does not produce a dependable top-K. We thus reframe PRP reranking as active learning from noisy pairwise comparisons and show that active rankers are drop-in replacements that improve NDCG@10 per call in the call-constrained regime. Our noise-robust framework also introduces a randomized-direction oracle that uses a single LLM call per pair. This approach converts systematic position bias into zero-mean noise, enabling unbiased aggregate ranking without the cost of bidirectional calls.

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.

Learning-to-Rank (LTR) is a supervised machine learning approach that constructs models specifically designed to order a set of items or documents based on their relevance or importance to a given query or context. Despite significant success in real-world information retrieval systems, current LTR methods rely on one prefix ranking metric (e.g., such as Normalized Discounted Cumulative Gain (NDCG) or Mean Average Precision (MAP)) for optimizing the ranking objective function. Such metric-dependent setting limits LTR methods from two perspectives: (1) non-differentiable problem: directly optimizing ranking functions over a given ranking metric is inherently non-smooth, making the training process unstable and inefficient; (2) limited ranking utility: optimizing over one single metric makes it difficult to generalize well to other ranking metrics of interest. To address the above issues, we propose a novel listwise LTR framework for efficient and generalizable ranking purpose. Specifically, we propose a new differentiable ranking loss that combines a smooth approximation to the ranking operator with the average mean square loss per query. Then, we adapt gradient-boosting machines to minimize our proposed loss with respect to each list, a novel contribution. Finally, extensive experimental results confirm that our method outperforms the current state-of-the-art in information retrieval measures with similar efficiency.