CLR-DRNets: Curriculum Learning with Restarts to Solve Visual Combinatorial Games

Authors Yiwei Bai, Di Chen, Carla P. Gomes

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Author Details

Yiwei Bai
  • Cornell University, Ithaca, NY, USA
Di Chen
  • Cornell University, Ithaca, NY, USA
Carla P. Gomes
  • Cornell University, Ithaca, NY, USA


We want to thank Wenting Zhao and anonymous reviewers for their valuable feedback.

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Yiwei Bai, Di Chen, and Carla P. Gomes. CLR-DRNets: Curriculum Learning with Restarts to Solve Visual Combinatorial Games. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We introduce a curriculum learning framework for challenging tasks that require a combination of pattern recognition and combinatorial reasoning, such as single-player visual combinatorial games. Our work harnesses Deep Reasoning Nets (DRNets) [Chen et al., 2020], a framework that combines deep learning with constraint reasoning for unsupervised pattern demixing. We propose CLR-DRNets (pronounced Clear-DRNets), a curriculum-learning-with-restarts framework to boost the performance of DRNets. CLR-DRNets incrementally increase the difficulty of the training instances and use restarts, a new model selection method that selects multiple models from the same training trajectory to learn a set of diverse heuristics and apply them at inference time. An enhanced reasoning module is also proposed for CLR-DRNets to improve the ability of reasoning and generalize to unseen instances. We consider Visual Sudoku, i.e., Sudoku with hand-written digits or letters, and Visual Mixed Sudoku, a substantially more challenging task that requires the demixing and completion of two overlapping Visual Sudokus. We propose an enhanced reasoning module for the DRNets framework for encoding these visual games We show how CLR-DRNets considerably outperform DRNets and other approaches on these visual combinatorial games.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Machine learning
  • Unsupervised Learning
  • Combinatorial Optimization


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