# OpenBlock: Constructive and Verified Content Generation for Adaptive Tile-Matching Games

arXiv: https://arxiv.org/abs/2609.22177 · HTML: https://mlsanity.com/paper/2609.22177/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Reinforcement Learning with Unsupervised Auxiliary Tasks](https://mlsanity.com/paper/1611.05397/) (2016)
- [Automatic Curriculum Learning For Deep RL: A Short Survey](https://mlsanity.com/paper/2003.04664/) (2020)
- [Procedural Content Generation via Machine Learning (PCGML)](https://mlsanity.com/paper/1702.00539/) (2017)
- [Deep Learning for Procedural Content Generation](https://mlsanity.com/paper/2010.04548/) (2020)
- [Verification-Guided Shielding for Deep Reinforcement Learning](https://mlsanity.com/paper/2406.06507/) (2024)
- [What makes useful auxiliary tasks in reinforcement learning: investigating the effect of the target policy](https://mlsanity.com/paper/2204.00565/) (2022)
- [DL-DDA -- Deep Learning based Dynamic Difficulty Adjustment with UX and Gameplay constraints](https://mlsanity.com/paper/2106.03075/) (2021)
- [The Game of Tetris in Machine Learning](https://mlsanity.com/paper/1905.01652/) (2019)
- [Continuous Reinforcement Learning-based Dynamic Difficulty Adjustment in a Visual Working Memory Game](https://mlsanity.com/paper/2308.12726/) (2023)

## Abstract (arXiv)

Tile-matching puzzle games serve hundreds of millions of players, yet the content-generation algorithms that decide which pieces to present at each turn remain proprietary, and no open platform exists for studying adaptive difficulty in this genre. We present an adaptive tile-matching platform whose central algorithmic contribution is a dual-track content-generation architecture: a deterministic rule-based generator that is always available, and an optional learned generator, both subject to a common verification gate that establishes, by exhaustive sequential-placement search, that every delivered piece set is fully placeable so the learned track can never degrade the constructive-feasibility guarantee of the rule track. A self-play reinforcement-learning placement agent, supervised by auxiliary tasks that expose per-shape placeability to shared representations, is used to diagnose the game's dominant failure mode: at high board fill, long-bar pieces lose the majority of their legal placements. Across 234,000+ self-play episodes the agent reaches a 35.6% win rate (median score 4,200), and controlled simulation shows that at board fill rates of 70--75%, 33--56% of long-bar pieces have no legal placement, while spawn difficulty distributions are statistically indistinguishable between won and lost games---evidence that board-state degeneration, not content difficulty, drives late-game failure. Head-to-head ablations show that per-shape placeability supervision---not aggregate difficulty features---drives the representation gain, and a 14-day online gray rollout (48,000 players; sample-ratio verified, CUPED-adjusted) lifts day-1 retention by 1.8 percentage points and session duration by 7% over the rule track alone, quantifying the neural track's asymmetric upside in live play.