TSPRank: Bridging Pairwise and Listwise Methods with a Bilinear Travelling Salesman Model

TL;DR

TSPRank reframes position-based ranking as a Travelling Salesman Problem to bridge pairwise and listwise LETOR approaches. By learning a bilinear edge scoring function atop an optional encoder, and solving an exact MILP for the ranking permutation, the method captures global information while leveraging local pairwise signals. The authors present local and global learning schemes, integrate TSP solving into training, and demonstrate robust gains across stock ranking, information retrieval, and historical event ordering with diverse backbones. Inference latency is analyzed, highlighting tradeoffs between accuracy and computational overhead, and suggesting regimes where the approach yields practical benefits. Overall, TSPRank offers a versatile, backbone-agnostic enhancement for ordinal ranking tasks with strong cross-domain performance.

Abstract

Traditional Learning-To-Rank (LETOR) approaches, including pairwise methods like RankNet and LambdaMART, often fall short by solely focusing on pairwise comparisons, leading to sub-optimal global rankings. Conversely, deep learning based listwise methods, while aiming to optimise entire lists, require complex tuning and yield only marginal improvements over robust pairwise models. To overcome these limitations, we introduce Travelling Salesman Problem Rank (TSPRank), a hybrid pairwise-listwise ranking method. TSPRank reframes the ranking problem as a Travelling Salesman Problem (TSP), a well-known combinatorial optimisation challenge that has been extensively studied for its numerous solution algorithms and applications. This approach enables the modelling of pairwise relationships and leverages combinatorial optimisation to determine the listwise ranking. This approach can be directly integrated as an additional component into embeddings generated by existing backbone models to enhance ranking performance. Our extensive experiments across three backbone models on diverse tasks, including stock ranking, information retrieval, and historical events ordering, demonstrate that TSPRank significantly outperforms both pure pairwise and listwise methods. Our qualitative analysis reveals that TSPRank's main advantage over existing methods is its ability to harness global information better while ranking. TSPRank's robustness and superior performance across different domains highlight its potential as a versatile and effective LETOR solution.

Figures (5)

• Figure 1: Illustration of TSPRank and the complete pipeline of local and global learning. The pipeline starts with a Transformer Encoder or any embeddings generated from another existing Backbone Model, followed by a Bilinear Model generating pairwise scores to form an Adjacency Matrix. Local learning compares the predicted matrix with the ground truth to calculate the local loss $\mathcal{L}_{local}$. Global learning uses the max-margin loss $\mathcal{L}_{glob}$ to incorporate the Gurobi TSP solver during training.
• Figure 2: Visualisation of predictions by LambdaMART, Rankformer, and TSPRank-Global on the constructed group. Numbers in parentheses indicate the true ranking.
• Figure 3: Illustration of the intra-country pairwise comparison graph. Edges between pairs of events from different countries are omitted for clarity. Scores highlighted in red indicate errors in the pairwise prediction for TSPRank-Global.
• Figure 4: Visualisation of the model predictions on additional groups. Numbers in parentheses indicate the true ranking.
• Figure 5: Mean inference time per ranking group for TSPRank and Rankformer on OTD2 across group sizes of 5, 10, 30, 50, and 100. The blue (TSPRank solver only) and red (TSPRank) lines overlap with minor differences.