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An Empirical Comparison of Cost Functions in Inductive Logic Programming

arXiv 2503.07554 ↗First posted 10 Mar 2025cs.LGcited by 0

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Abstract (arXiv)

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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References · 22

  1. 2016Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotationscited by 2,656
  2. 2017Learning Explanatory Rules from Noisy Datacited by 211
  3. 2023Hypothesis Search: Inductive Reasoning with Language Modelscited by 120
  4. 2023The ConceptARC Benchmark: Evaluating Understanding and Generalization in the ARC Domaincited by 101
  5. 2020Inductive logic programming at 30: a new introductioncited by 85
  6. 2023LLMs and the Abstraction and Reasoning Corpus: Successes, Failures, and the Importance of Object-based Representationscited by 82
  7. 2020Learning programs by learning from failurescited by 73
  8. 2013A Semantic Matching Energy Function for Learning with Multi-relational Datacited by 61
  9. 2019Few-Shot Bayesian Imitation Learning with Logical Program Policiescited by 30
  10. 2020BUSTLE: Bottom-Up Program Synthesis Through Learning-Guided Explorationcited by 30
  11. 2019Making sense of sensory inputcited by 29
  12. 2021Neuro-Symbolic Hierarchical Rule Inductioncited by 23
10 more
  1. 2018Inductive Learning of Answer Set Programs from Noisy Examplescited by 22
  2. 2020Randomised Gaussian Process Upper Confidence Bound for Bayesian Optimisationcited by 22
  3. 2019Inductive general game playingcited by 18
  4. 2020Just-in-Time Learning for Bottom-Up Enumerative Synthesiscited by 18
  5. 2023Learning MDL logic programs from noisy datacited by 15
  6. 2024Optimal or Greedy Decision Trees? Revisiting their Objectives, Tuning, and Performancecited by 9
  7. 2020Inductive Program Synthesis Over Noisy Datacited by 7
  8. 2022Learning logic programs by combining programscited by 7
  9. 2023Program Synthesis with Best-First Bottom-Up Searchcited by 7
  10. 2024Relational decomposition for program synthesiscited by 6

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