## Abstract

This paper resolves the open question of designing near-optimal algorithms for learning imperfect-information extensive-form games from bandit feedback. We present the first line of algorithms that require only O^{e}((XA + Y B)/ε^{2}) episodes of play to find an ε-approximate Nash equilibrium in two-player zero-sum games, where X, Y are the number of information sets and A, B are the number of actions for the two players. This improves upon the best known sample complexity of O^{e}((X^{2}A + Y ^{2}B)/ε^{2}) by a factor of O^{e}(max(X, Y )), and matches the information-theoretic lower bound up to logarithmic factors. We achieve this sample complexity by two new algorithms: Balanced Online Mirror Descent, and Balanced Counterfactual Regret Minimization. Both algorithms rely on novel approaches of integrating balanced exploration policies into their classical counterparts. We also extend our results to learning Coarse Correlated Equilibria in multi-player general-sum games.

Original language | English (US) |
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Pages (from-to) | 1337-1382 |

Number of pages | 46 |

Journal | Proceedings of Machine Learning Research |

Volume | 162 |

State | Published - 2022 |

Event | 39th International Conference on Machine Learning, ICML 2022 - Baltimore, United States Duration: Jul 17 2022 → Jul 23 2022 |

## All Science Journal Classification (ASJC) codes

- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability