Preference Optimization for Combinatorial Optimization Problems
Keywords: Combinatorial Optimization, Reinforcement Learning, Preference-Based Reinforcement Learning
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 optimal solutions. Despite significant progress, existing RL approaches face challenges such as diminishing reward signals and inefficient exploration in vast combinatorial action spaces, leading to inefficient learning. In this paper, we propose $Preference
\ Optimization (PO)$, a novel framework that transforms quantitative reward signals into qualitative preference signals via statistical comparison modeling, emphasizing the superiority among generated solutions. Methodologically, by reparameterizing the reward function in terms of policy probabilities and utilizing preference models like Bradley-Terry and Thurstone, we formulate an entropy-regularized optimization objective that aligns the policy directly with preferences while avoiding intractable computations. Furthermore, we integrate heuristic local search techniques into the fine-tuning process to generate high-quality preference pairs, helping the policy escape local optima. Empirical results on standard combinatorial optimization 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 outperforms traditional RL algorithms, achieving superior sample efficiency and solution quality. Our work offers a simple yet efficient algorithmic advancement in neural combinatorial optimization.
Supplementary Material: zip
Primary Area: optimization
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Submission Number: 1610
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