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Markov Senior -- Learning Markov Junior Grammars to Generate User-specified Content

Mehmet Kayra Oğuz, Alexander Dockhorn

TL;DR

Markov Senior introduces a genetic programming framework to automatically learn Markov Junior grammars from a single example, addressing the reliance on handcrafted rule sets in procedural content generation. By extracting pattern relations and enforcing relation-bounded rules, the method narrows the search space, while a two-stage evolutionary process and a divide-and-conquer strategy enable scalable generation of content that matches the input sample. The approach uses a KL-divergence-based fitness to maximize coherence with the example and demonstrates applicability to both image-like patterns and Super Mario levels, indicating versatility across domains. While showing promising results, the paper acknowledges limitations and emphasizes future work on parameter analysis, improved operators, and user-controlled trade-offs between novelty and coherence, with a public codebase to foster further development.

Abstract

Markov Junior is a probabilistic programming language used for procedural content generation across various domains. However, its reliance on manually crafted and tuned probabilistic rule sets, also called grammars, presents a significant bottleneck, diverging from approaches that allow rule learning from examples. In this paper, we propose a novel solution to this challenge by introducing a genetic programming-based optimization framework for learning hierarchical rule sets automatically. Our proposed method ``Markov Senior'' focuses on extracting positional and distance relations from single input samples to construct probabilistic rules to be used by Markov Junior. Using a Kullback-Leibler divergence-based fitness measure, we search for grammars to generate content that is coherent with the given sample. To enhance scalability, we introduce a divide-and-conquer strategy that enables the efficient generation of large-scale content. We validate our approach through experiments in generating image-based content and Super Mario levels, demonstrating its flexibility and effectiveness. In this way, ``Markov Senior'' allows for the wider application of Markov Junior for tasks in which an example may be available, but the design of a generative rule set is infeasible.

Markov Senior -- Learning Markov Junior Grammars to Generate User-specified Content

TL;DR

Markov Senior introduces a genetic programming framework to automatically learn Markov Junior grammars from a single example, addressing the reliance on handcrafted rule sets in procedural content generation. By extracting pattern relations and enforcing relation-bounded rules, the method narrows the search space, while a two-stage evolutionary process and a divide-and-conquer strategy enable scalable generation of content that matches the input sample. The approach uses a KL-divergence-based fitness to maximize coherence with the example and demonstrates applicability to both image-like patterns and Super Mario levels, indicating versatility across domains. While showing promising results, the paper acknowledges limitations and emphasizes future work on parameter analysis, improved operators, and user-controlled trade-offs between novelty and coherence, with a public codebase to foster further development.

Abstract

Markov Junior is a probabilistic programming language used for procedural content generation across various domains. However, its reliance on manually crafted and tuned probabilistic rule sets, also called grammars, presents a significant bottleneck, diverging from approaches that allow rule learning from examples. In this paper, we propose a novel solution to this challenge by introducing a genetic programming-based optimization framework for learning hierarchical rule sets automatically. Our proposed method ``Markov Senior'' focuses on extracting positional and distance relations from single input samples to construct probabilistic rules to be used by Markov Junior. Using a Kullback-Leibler divergence-based fitness measure, we search for grammars to generate content that is coherent with the given sample. To enhance scalability, we introduce a divide-and-conquer strategy that enables the efficient generation of large-scale content. We validate our approach through experiments in generating image-based content and Super Mario levels, demonstrating its flexibility and effectiveness. In this way, ``Markov Senior'' allows for the wider application of Markov Junior for tasks in which an example may be available, but the design of a generative rule set is infeasible.
Paper Structure (18 sections, 4 equations, 9 figures)

This paper contains 18 sections, 4 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Background
  3. The Markov Algorithm and Markov Junior
  4. Markov Junior
  5. Genetic Programming
  6. Evaluation of Procedural Content Generation
  7. Related Work on Sample-based PCG
  8. Markov Senior - Learning Markov Junior Programs By Example
  9. $1^{st}$ Stage - Preprocessing
  10. Pattern Relations
  11. Creating Relation-bounded Rules
  12. $2^{nd}$ Stage - Evolutionary Optimization
  13. Representation and Generation of Markov Junior Grammars
  14. Genetic Modifications of Markov Junior Grammars
  15. Measuring the Fitness
  16. ...and 3 more sections

Figures (9)

  • Figure 1: Examples of Markov Junior grammars and their output taken from MarkovJunior.
  • Figure 2: An overview of the whole evolutionary process.
  • Figure 3: Initializing a Mario level based on the given sample.
  • Figure 4: $1^{\textit{st}}$ Stage - Scanning a sample with an $n \times n$ window.
  • Figure 5: $1^{\textit{st}}$ Stage - Pattern extraction, rule generation, and application.
  • ...and 4 more figures