# Toward a Metrology for Artificial Intelligence: Hidden-Rule Environments and Reinforcement Learning

arXiv: https://arxiv.org/abs/2509.06213 · HTML: https://mlsanity.com/paper/2509.06213/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 7 Sep 2025.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 8 of 8)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [The ConceptARC Benchmark: Evaluating Understanding and Generalization in the ARC Domain](https://mlsanity.com/paper/2305.07141/) (2023)
- [Large Language Models Are Not Strong Abstract Reasoners](https://mlsanity.com/paper/2305.19555/) (2023)
- [The Game of Hidden Rules: A New Kind of Benchmark Challenge for Machine Learning](https://mlsanity.com/paper/2207.10218/) (2022)
- [Can We Distinguish Machine Learning from Human Learning?](https://mlsanity.com/paper/1910.03466/) (2019)
- [Comparing Reinforcement Learning and Human Learning using the Game of Hidden Rules](https://mlsanity.com/paper/2306.17766/) (2023)

## Built on by (most cited first, 1 of 1)

- [AI Learning and Conceptual Transfer in the Game of Hidden Rules](https://mlsanity.com/paper/2608.21372/) (2026)

## Abstract (arXiv)

We investigate reinforcement learning in the Game Of Hidden Rules (GOHR) environment, a complex puzzle in which an agent must infer and execute hidden rules to clear a 6×6 board by placing game pieces into buckets. We explore two state representation strategies, namely Feature-Centric (FC) and Object-Centric (OC), and employ a Transformer-based Advantage Actor-Critic (A2C) algorithm for training. The agent has access only to partial observations and must simultaneously infer the governing rule and learn the optimal policy through experience. We evaluate our models across multiple rule-based and trial-list-based experimental setups, analyzing transfer effects and the impact of representation on learning efficiency.