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arXiv 2209.03393cs.AIcs.LG
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NP-难搜索问题的启发式逼近器(Un)Scalability

The (Un)Scalability of Heuristic Approximators for NP-Hard Search Problems

Texas A&M University(德州农工大学);University of Southern California(南加州大学)

Sumedh Pendurkar, Taoan Huang, Sven Koenig, Guni Sharon

摘要:

A* 算法通常用于解决NP难的组合优化问题。当给定完全信息启发式函数时,A* 在分支因子和最小代价路径边数的时间多项式中求解了许多NP-难的最小代价路径问题,因此,高精度地逼近它们的完全信息启发式函数是NP-难的.因此,我们检查最近的出版物,提出使用神经网络为此目的。我们支持我们的主张,这些方法不扩展到大的实例大小的理论和实验。我们的第一个实验结果为三个代表性的NP-难最小成本路径问题表明,使用神经网络近似完全知情的启发式功能,具有高精度可能会导致网络的规模,规模指数的实例大小。因此,研究团体可能会从研究将启发式搜索与机器学习集成的其他方法中受益。

英文摘要:

The A* algorithm is commonly used to solve NP-hard combinatorial optimization problems. When provided with a completely informed heuristic function, A* solves many NP-hard minimum-cost path problems in time polynomial in the branching factor and the number of edges in a minimum-cost path. Thus, approximating their completely informed heuristic functions with high precision is NP-hard. We therefore examine recent publications that propose the use of neural networks for this purpose. We support our claim that these approaches do not scale to large instance sizes both theoretically and experimentally. Our first experimental results for three representative NP-hard minimum-cost path problems suggest that using neural networks to approximate completely informed heuristic functions with high precision might result in network sizes that scale exponentially in the instance sizes. The research community might thus benefit from investigating other ways of integrating heuristic search with machine learning.

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