AI解法在最大独立集问题上竟不如传统算法,连最简单的贪心法都常被超越。
Unrealized Expectations: Comparing AI Methods vs Classical Algorithms for Maximum Independent Set
- 用序列化分析发现AI方法实际推理方式类似简单贪心,效率更低
- 顶尖AI方法在随机图上仍远逊于单核CPU的KaMIS求解器
- 适合关注经典算法与AI对比、或需可靠优化解的研究者阅读
近年来,生成模型和强化学习等AI方法被用于组合优化(CO)问题,尤其是NP难问题。本文在最大独立集(MIS)问题上,将基于GPU的AI方法与基于CPU的经典方法进行对比。令人惊讶的是,在分布内随机图上,领先的AI方法始终被单核CPU运行的先进求解器KaMIS超越,部分AI方法甚至无法超过最简单的度贪心启发式。即使采用局部搜索等后处理技术,AI方法表现仍不及CPU求解器。为理解失败原因,我们提出新型分析方法‘序列化’,揭示非回溯型AI方法(如基于GFlowNets的LTFT)的推理机制与度贪心相似,因而效果更差。研究提示应重新审视当前AI在组合优化中的方法,倡导更严格的基准测试及经典启发式与AI的合理融合。此外,我们发现KaMIS在稀疏随机图上表现优异,表明Coja-Oghlan & Efthymiou(2015)提出的关于大规模独立集的破碎阈值猜想不适用于真实规模(如10^6节点)。
原文摘要 · Abstract (English)
AI methods, such as generative models and reinforcement learning, have recently been applied to combinatorial optimization (CO) problems, especially NP-hard ones. This paper compares such GPU-based methods with classical CPU-based methods on the Maximum Independent Set (MIS) problem. Strikingly, even on in-distribution random graphs, leading AI-inspired methods are consistently outperformed by the state-of-the-art classical solver KaMIS running on a single CPU, and some AI-inspired methods frequently fail to surpass even the simplest degree-based greedy heuristic. Even with post-processing techniques like local search, AI-inspired methods still perform worse than CPU-based solvers. To better understand the source of these failures, we introduce a novel analysis, serialization, which reveals that non-backtracking AI-inspired methods, e.g. LTFT (which is based on GFlowNets), end up reasoning similarly to the simplest degree-based greedy, and thus worse than KaMIS. More generally, our findings suggest a need for a rethinking of current approaches in AI for CO, advocating for more rigorous benchmarking and the principled integration of classical heuristics. Additionally, we also find that CPU-based algorithm KaMIS have strong performance on sparse random graphs, which appears to show that the shattering threshold conjecture for large independent sets proposed by Coja-Oghlan & Efthymiou (2015) does not apply for real-life sizes (such as 10^6 nodes).
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