Open-ended learning in symmetric zero-sum games
David Balduzzi, Marta Garnelo, Yoram Bachrach, Wojciech Czarnecki, Julien Perolat, Max Jaderberg, Thore Graepel
Abstract
Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them ‘winner’ and ‘loser’. If the game is approximately transitive, then self-play generates sequences of agents of increasing strength. However, nontransitive games, such as rock-paper-scissors, can exhibit strategic cycles, and there is no longer a clear objective – we want agents to increase in strength, but against whom is unclear. In this paper, we introduce a geometric framework for formulating agent objectives in zero-sum games, in order to construct adaptive sequences of objectives that yield open-ended learning. The framework allows us to reason about population performance in nontransitive games, and enables the development of a new algorithm (rectified Nash response, PSRO_rN) that uses game-theoretic niching to construct diverse populations of effective agents, producing a stronger set of agents than existing algorithms. We apply PSRO_rN to two highly nontransitive resource allocation games and find that PSRO_rN consistently outperforms the existing alternatives.
BibTeX
@InProceedings{pmlr-v97-balduzzi19a,
title = {Open-ended learning in symmetric zero-sum games},
author = {Balduzzi, David and Garnelo, Marta and Bachrach, Yoram and Czarnecki, Wojciech and Perolat, Julien and Jaderberg, Max and Graepel, Thore},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {434--443},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/balduzzi19a/balduzzi19a.pdf},
url = {https://proceedings.mlr.press/v97/balduzzi19a.html},
abstract = {Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them ‘winner’ and ‘loser’. If the game is approximately transitive, then self-play generates sequences of agents of increasing strength. However, nontransitive games, such as rock-paper-scissors, can exhibit strategic cycles, and there is no longer a clear objective – we want agents to increase in strength, but against whom is unclear. In this paper, we introduce a geometric framework for formulating agent objectives in zero-sum games, in order to construct adaptive sequences of objectives that yield open-ended learning. The framework allows us to reason about population performance in nontransitive games, and enables the development of a new algorithm (rectified Nash response, PSRO_rN) that uses game-theoretic niching to construct diverse populations of effective agents, producing a stronger set of agents than existing algorithms. We apply PSRO_rN to two highly nontransitive resource allocation games and find that PSRO_rN consistently outperforms the existing alternatives.}
}