### Abstract

Markov games is a framework which can be used to formalise n-agent reinforcement learning (RL). Littman (Markov games as a framework for multi-agent reinforcement learning, in: Proceedings of the 11th International Conference on Machine Learning (ICML-94), 1994.) uses this framework to model two-agent zero-sum problems and, within this context, proposes the minimax-Q algorithm. This paper reviews RL algorithms for two-player zero-sum Markov games and introduces a new, simple, fast. algorithm, called 2L(2).2L(2) is compared to several standard algorithms (Q-learning, Minimax and minimax-Q) implemented with the)ash library written in Python. The experiments show that 222 converges empirically to optimal mixed policies, as minimax-Q, but uses a surprisingly simple and cheap updating rule. (C) 2009 Elsevier B.V. All rights reserved.

Original language | English |
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Title of host publication | Proceedings of the 16th European Symposium on Artificial Neural Networks |

Pages | 137-142 |

Number of pages | 6 |

Publication status | Published - 2009 |

Externally published | Yes |

Event | 16th European Symposium on Artificial Neural Networks - Advances in Computational Intelligence and Learning, ESANN 2008 - Bruges, Belgium Duration: 23 Apr 2008 → 25 Apr 2008 |

### Conference

Conference | 16th European Symposium on Artificial Neural Networks - Advances in Computational Intelligence and Learning, ESANN 2008 |
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Country | Belgium |

City | Bruges |

Period | 23/04/08 → 25/04/08 |

### Keywords

- Reinforcement Learning Q-learning Markov Games Two-player Zero-sum Games Multi-agent

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## Cite this

Frénay, B., & Saerens, M. (2009). QL2, a simple reinforcement learning scheme for two-player zero-sum Markov games: Proceedings of the 16th European Symposium on Artificial Neural Networks. In

*Proceedings of the 16th European Symposium on Artificial Neural Networks*(pp. 137-142)