BQ-NCO：用于高效神经组合优化的互模拟商化
BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization
AI总结：
本文提出BQ-MDP，利用互模拟商化约简组合优化MDP状态并保持最优性，结合注意力策略网络模仿学习，在五类问题上实现大规模分布外泛化的SOTA结果。
摘要：
尽管基于神经的组合优化方法在端到端启发式学习方面取得了成功，但分布外泛化仍是一项挑战。本文提出一种将组合优化问题（COPs）表述为马尔可夫决策过程（MDPs）的新颖形式，可有效利用COPs的常见对称性以提升分布外鲁棒性。从构造性方法的直接MDP表述出发，我们基于MDP中的互模拟商化（Bisimulation Quotienting，BQ）引入了一种通用的状态空间约简方法。随后，针对具有递归性质的COPs，我们对互模拟进行专门化，并展示约简状态如何利用这些问题的对称性并促进MDP求解。我们的方法具有原则性，并且证明了所提出BQ-MDP的最优策略实际上能够求解相关COPs。我们在五个经典问题上阐释该方法：欧几里得旅行商、非对称旅行商、带容量车辆路径、定向运动和背包问题。此外，针对每个问题，我们为BQ-MDP引入一个简单的基于注意力的策略网络，通过模仿来自单一分布的小规模实例的（近）最优解进行训练。我们在合成与现实基准上均取得五个COPs的最新最优结果。值得注意的是，与多数现有神经方法不同，所学策略在无需任何额外搜索过程的情况下，对远大于训练期间所见规模的实例表现出优异的泛化性能。
英文摘要：
Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization Problems (COPs) as Markov Decision Processes (MDPs) that effectively leverages common symmetries of COPs to improve out-of-distribution robustness. Starting from a direct MDP formulation of a constructive method, we introduce a generic way to reduce the state space, based on Bisimulation Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize the bisimulation and show how the reduced state exploits the symmetries of these problems and facilitates MDP solving. Our approach is principled and we prove that an optimal policy for the proposed BQ-MDP actually solves the associated COPs. We illustrate our approach on five classical problems: the Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing, Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce a simple attention-based policy network for the BQ-MDPs, which we train by imitation of (near) optimal solutions of small instances from a single distribution. We obtain new state-of-the-art results for the five COPs on both synthetic and realistic benchmarks. Notably, in contrast to most existing neural approaches, our learned policies show excellent generalization performance to much larger instances than seen during training, without any additional search procedure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
