Preference Optimization for Combinatorial Optimization Problems

• URL: http://arxiv.org/abs/2505.08735v1
• Date: Tue, 13 May 2025 16:47:00 GMT
• Title: Preference Optimization for Combinatorial Optimization Problems
• Authors: Mingjun Pan, Guanquan Lin, You-Wei Luo, Bin Zhu, Zhien Dai, Lijun Sun, Chun Yuan,
• Abstract summary: Reinforcement Learning (RL) has emerged as a powerful tool for neural optimization, enabling models learns that solve complex problems without requiring expert knowledge.<n>Despite significant progress, existing RL approaches face challenges such as diminishing reward signals and inefficient exploration in vast action spaces.<n>We propose Preference Optimization, a novel method that transforms quantitative reward signals into qualitative preference signals via statistical comparison modeling.
• Score: 54.87466279363487
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Reinforcement Learning (RL) has emerged as a powerful tool for neural combinatorial optimization, enabling models to learn heuristics that solve complex problems without requiring expert knowledge. Despite significant progress, existing RL approaches face challenges such as diminishing reward signals and inefficient exploration in vast combinatorial action spaces, leading to inefficiency. In this paper, we propose Preference Optimization, a novel method that transforms quantitative reward signals into qualitative preference signals via statistical comparison modeling, emphasizing the superiority among sampled solutions. Methodologically, by reparameterizing the reward function in terms of policy and utilizing preference models, we formulate an entropy-regularized RL objective that aligns the policy directly with preferences while avoiding intractable computations. Furthermore, we integrate local search techniques into the fine-tuning rather than post-processing to generate high-quality preference pairs, helping the policy escape local optima. Empirical results on various benchmarks, such as the Traveling Salesman Problem (TSP), the Capacitated Vehicle Routing Problem (CVRP) and the Flexible Flow Shop Problem (FFSP), demonstrate that our method significantly outperforms existing RL algorithms, achieving superior convergence efficiency and solution quality.

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