Aggregating a consensus ranking from multiple input rankings is a fundamental problem with applications in recommendation systems, search engines, job recruitment, and elections. Despite decades of research in consensus ranking aggregation, minimizing the Kemeny distance remains computationally intractable. Specifically, determining an optimal aggregation of rankings with respect to the Kemeny distance is an NP-hard problem, limiting its practical application to relatively small-scale instances. We propose the Kemeny Transformer, a novel Transformer-based algorithm trained via reinforcement learning to efficiently approximate the Kemeny optimal ranking. Experimental results demonstrate that our model outperforms classical majority-heuristic and Markov-chain approaches, achieving substantially faster inference than integer linear programming solvers. Our approach thus offers a practical, scalable alternative for real-world ranking-aggregation tasks.

翻译：从多个输入排序中聚合出共识排序是一个基础性问题，在推荐系统、搜索引擎、职位招聘和选举等领域具有重要应用。尽管共识排序聚合研究已有数十年历史，但最小化Kemeny距离在计算上仍然难以处理。具体而言，确定关于Kemeny距离的最优排序聚合是一个NP难问题，这限制了其在实际中仅能应用于相对小规模的实例。我们提出了Kemeny Transformer，这是一种基于Transformer的新型算法，通过强化学习进行训练，能够高效逼近Kemeny最优排序。实验结果表明，我们的模型在性能上超越了经典的多数启发式方法和马尔可夫链方法，并且推理速度显著快于整数线性规划求解器。因此，我们的方法为现实世界的排序聚合任务提供了一种实用且可扩展的替代方案。