比较7种代价函数在归纳逻辑编程中的表现，发现最小化训练误差或描述长度效果最好。
An Empirical Comparison of Cost Functions in Inductive Logic Programming
- 扩展约束式ILP系统，支持7种标准代价函数的最优假设学习
- 在20多个领域1000个任务上验证，最小化训练误差或描述长度整体表现最优
- 揭示缩小假设规模未必降低泛化误差，为代价函数选择提供实证依据
近年来的归纳逻辑编程（ILP）方法致力于学习最优假设，即在训练数据上最小化特定代价函数的假设。常见的代价函数包括最小化训练误差、文本复杂度或假设的描述长度等。然而，如何选择合适的代价函数仍是关键挑战。为此，我们扩展了一种基于约束的ILP系统，使其能够针对七种标准代价函数学习最优假设，并在超过20个领域和1000个任务上对这些假设的泛化误差进行实证比较，涵盖游戏博弈、程序合成和图像推理等任务。结果表明，尽管没有一种代价函数在所有情况下都优于其他，但最小化训练误差或描述长度的整体表现最佳。值得注意的是，最小化假设规模并不总是能降低泛化误差。
原文摘要 · Abstract (English)
Recent inductive logic programming (ILP) approaches learn optimal hypotheses. An optimal hypothesis minimises a given cost function on the training data. There are many cost functions, such as minimising training error, textual complexity, or the description length of hypotheses. However, selecting an appropriate cost function remains a key question. To address this gap, we extend a constraint-based ILP system to learn optimal hypotheses for seven standard cost functions. We then empirically compare the generalisation error of optimal hypotheses induced under these standard cost functions. Our results on over 20 domains and 1000 tasks, including game playing, program synthesis, and image reasoning, show that, while no cost function consistently outperforms the others, minimising training error or description length has the best overall performance. Notably, our results indicate that minimising the size of hypotheses does not always reduce generalisation error.
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