# Optimality-based Analysis of XCSF Compaction in Discrete Reinforcement Learning

arXiv: https://arxiv.org/abs/2009.01476 · HTML: https://mlsanity.com/paper/2009.01476/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2020.

## Built on by (most cited first, 2 of 2)

- [Fuzzy-UCS Revisited: Self-Adaptation of Rule Representations in Michigan-Style Learning Fuzzy-Classifier Systems](https://mlsanity.com/paper/2505.06017/) (2025)
- [Pittsburgh Learning Classifier Systems for Explainable Reinforcement Learning: Comparing with XCS](https://mlsanity.com/paper/2305.09945/) (2023)

## Abstract (arXiv)

Learning classifier systems (LCSs) are population-based predictive systems that were originally envisioned as agents to act in reinforcement learning (RL) environments. These systems can suffer from population bloat and so are amenable to compaction techniques that try to strike a balance between population size and performance. A well-studied LCS architecture is XCSF, which in the RL setting acts as a Q-function approximator. We apply XCSF to a deterministic and stochastic variant of the FrozenLake8x8 environment from OpenAI Gym, with its performance compared in terms of function approximation error and policy accuracy to the optimal Q-functions and policies produced by solving the environments via dynamic programming. We then introduce a novel compaction algorithm (Greedy Niche Mass Compaction - GNMC) and study its operation on XCSF's trained populations. Results show that given a suitable parametrisation, GNMC preserves or even slightly improves function approximation error while yielding a significant reduction in population size. Reasonable preservation of policy accuracy also occurs, and we link this metric to the commonly used steps-to-goal metric in maze-like environments, illustrating how the metrics are complementary rather than competitive.