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arXiv 2109.14271cs.LGmath.COmath.OC
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(机器)学习提高离散算法的经验性能

(Machine) Learning to Improve the Empirical Performance of Discrete Algorithms

UC Davis Computer Science(加州大学戴维斯分校计算机科学);UC Davis Mathematics(加州大学戴维斯分校数学)

Imran Adham, Jesus De Loera, Zhenyang Zhang

摘要:

本文讨论了一个数据驱动的,基于算法的框架,使算法决策或建议,而无需专家知识。我们提高了两个算法的案例研究的性能:选择一个枢纽规则的单纯形方法和选择的所有对最短路径算法。我们训练机器学习方法,以在没有人类专家意见的情况下为给定数据选择最佳算法。我们使用两种类型的技术,神经网络和提升决策树。基于我们的实验,我们得出结论:1)我们的选择框架推荐了各种枢轴规则,这些规则与仅使用固定的默认枢轴规则相比,可以提高整体性能。多年来,专家们将最陡边枢轴规则确定为最受欢迎的枢轴规则。我们的数据分析证实,最陡边的迭代次数不超过4%,而最优选择证实了人类专家的知识,但这次的知识是使用机器学习获得的。在这里,我们的推荐系统在使用梯度提升树时是最好的。2)对于全对最短路径问题,训练的模型有很大的改进,我们的选择平均距离最优选择0.07%。结论似乎不受我们使用的机器学习方法的影响。我们试图对这两个算法问题进行并行分析,但很明显,它们存在内在差异。例如,在所有对最短路径问题中,图密度是一个合理的预测因子,但在单纯形方法中没有类似的单个参数用于决策。

英文摘要:

This paper discusses a data-driven, empirically-based framework to make algorithmic decisions or recommendations without expert knowledge. We improve the performance of two algorithmic case studies: the selection of a pivot rule for the Simplex method and the selection of an all-pair shortest paths algorithm. We train machine learning methods to select the optimal algorithm for given data without human expert opinion. We use two types of techniques, neural networks and boosted decision trees. We concluded, based on our experiments, that: 1) Our selection framework recommends various pivot rules that improve overall total performance over just using a fixed default pivot rule. Over many years experts identified steepest-edge pivot rule as a favorite pivot rule. Our data analysis corroborates that the number of iterations by steepest-edge is no more than 4 percent more than the optimal selection which corroborates human expert knowledge, but this time the knowledge was obtained using machine learning. Here our recommendation system is best when using gradient boosted trees. 2) For the all-pairs shortest path problem, the models trained made a large improvement and our selection is on average .07 percent away from the optimal choice. The conclusions do not seem to be affected by the machine learning method we used. We tried to make a parallel analysis of both algorithmic problems, but it is clear that there are intrinsic differences. For example, in the all-pairs shortest path problem the graph density is a reasonable predictor, but there is no analogous single parameter for decisions in the Simplex method.

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。

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