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Counterfactual regret minimization (CFR) is a family of iterative algorithms that are the most popular and, in practice, fastest approach to approximately solving large imperfect-information games. In this paper we introduce novel CFR…

Computer Science and Game Theory · Computer Science 2019-02-22 Noam Brown , Tuomas Sandholm

A dominant approach to solving large imperfect-information games is Counterfactural Regret Minimization (CFR). In CFR, many regret minimization problems are combined to solve the game. For very large games, abstraction is typically needed…

Machine Learning · Computer Science 2019-12-02 Ryan D'Orazio , Dustin Morrill , James R. Wright

In general, two-agent decision-making problems can be modeled as a two-player game, and a typical solution is to find a Nash equilibrium in such game. Counterfactual regret minimization (CFR) is a well-known method to find a Nash…

Computer Science and Game Theory · Computer Science 2020-12-07 Huale Li , Xuan Wang , Shuhan Qi , Jiajia Zhang , Yang Liu , Yulin Wu , Fengwei Jia

Counterfactual regret minimization (CFR) is a family of algorithms for effectively solving imperfect-information games. To enhance CFR's applicability in large games, researchers use neural networks to approximate its behavior. However,…

Machine Learning · Computer Science 2025-11-12 Hang Xu , Kai Li , Haobo Fu , Qiang Fu , Junliang Xing , Jian Cheng

Counterfactual Regret Minimization (CFR) and its variants developed based upon Regret Matching (RM) have been considered to be the best method to solve incomplete information extensive form games. In addition to RM and CFR, Fictitious Play…

Computer Science and Game Theory · Computer Science 2023-11-14 Qi Ju

Counterfactual regret minimization (CFR) is a popular method to deal with decision-making problems of two-player zero-sum games with imperfect information. Unlike existing studies that mostly explore for solving larger scale problems or…

Machine Learning · Computer Science 2020-09-15 Huale Li , Xuan Wang , Fengwei Jia , Yifan Li , Yulin Wu , Jiajia Zhang , Shuhan Qi

Counterfactual regret minimization (CFR) is an effective algorithm for solving extensive games with imperfect information (IIEGs). However, CFR is only allowed to be applied in known environments, where the transition function of the chance…

Computer Science and Game Theory · Computer Science 2024-10-30 Chen Qiu , Xuan Wang , Tianzi Ma , Yaojun Wen , Jiajia Zhang

Counterfactual Regret Minimization (CRF) is a fundamental and effective technique for solving Imperfect Information Games (IIG). However, the original CRF algorithm only works for discrete state and action spaces, and the resulting strategy…

Artificial Intelligence · Computer Science 2018-12-31 Hui Li , Kailiang Hu , Zhibang Ge , Tao Jiang , Yuan Qi , Le Song

In two-player zero-sum games, if both players minimize their average external regret, then the average of the strategy profiles converges to a Nash equilibrium. For n-player general-sum games, however, theoretical guarantees for regret…

Computer Science and Game Theory · Computer Science 2013-05-02 Richard Gibson

Counterfactual regret minimization (CFR) is the most popular algorithm on solving two-player zero-sum extensive games with imperfect information and achieves state-of-the-art performance in practice. However, the performance of CFR is not…

Machine Learning · Computer Science 2018-12-27 Yichi Zhou , Tongzheng Ren , Jialian Li , Dong Yan , Jun Zhu

Counterfactual Regret Minimization (CFR) is the leading framework for solving large imperfect-information games. It converges to an equilibrium by iteratively traversing the game tree. In order to deal with extremely large games,…

Artificial Intelligence · Computer Science 2019-05-23 Noam Brown , Adam Lerer , Sam Gross , Tuomas Sandholm

No-regret learning has emerged as a powerful tool for solving extensive-form games. This was facilitated by the counterfactual-regret minimization (CFR) framework, which relies on the instantiation of regret minimizers for simplexes at each…

Computer Science and Game Theory · Computer Science 2017-11-10 Gabriele Farina , Christian Kroer , Tuomas Sandholm

Regret minimization is a powerful tool for solving large-scale extensive-form games. State-of-the-art methods rely on minimizing regret locally at each decision point. In this work we derive a new framework for regret minimization on…

Computer Science and Game Theory · Computer Science 2018-09-11 Gabriele Farina , Christian Kroer , Tuomas Sandholm

Counterfactual Regret Minimization (CFR) is an efficient no-regret learning algorithm for decision problems modeled as extensive games. CFR's regret bounds depend on the requirement of perfect recall: players always remember information…

Computer Science and Game Theory · Computer Science 2012-05-04 Marc Lanctot , Richard Gibson , Neil Burch , Martin Zinkevich , Michael Bowling

Counterfactual Regret Minimization (CFR)} is the popular method for finding approximate Nash equilibrium in two-player zero-sum games with imperfect information. CFR solves games by travsersing the full game tree iteratively, which limits…

Artificial Intelligence · Computer Science 2022-01-04 Huale Li , Xuan Wang , Zengyue Guo , Jiajia Zhang , Shuhan Qi

Regret minimization is a powerful tool for solving large-scale problems; it was recently used in breakthrough results for large-scale extensive-form game solving. This was achieved by composing simplex regret minimizers into an overall…

Machine Learning · Computer Science 2019-02-19 Gabriele Farina , Christian Kroer , Tuomas Sandholm

A considerable chasm has been looming for decades between theory and practice in zero-sum game solving through first-order methods. Although a convergence rate of $T^{-1}$ has long been established, the most effective paradigm in practice…

Computer Science and Game Theory · Computer Science 2026-02-18 Brian Hu Zhang , Ioannis Anagnostides , Tuomas Sandholm

Regret minimization has proved to be a versatile tool for tree-form sequential decision making and extensive-form games. In large two-player zero-sum imperfect-information games, modern extensions of counterfactual regret minimization (CFR)…

Computer Science and Game Theory · Computer Science 2021-03-09 Gabriele Farina , Tuomas Sandholm

Counterfactual Regret Minimization and variants (e.g. Public Chance Sampling CFR and Pure CFR) have been known as the best approaches for creating approximate Nash equilibrium solutions for imperfect information games such as poker. This…

Computer Science and Game Theory · Computer Science 2014-07-21 Oskari Tammelin

Regret-based algorithms are highly efficient at finding approximate Nash equilibria in sequential games such as poker games. However, most regret-based algorithms, including counterfactual regret minimization (CFR) and its variants, rely on…

Machine Learning · Computer Science 2021-10-28 Chung-Wei Lee , Christian Kroer , Haipeng Luo
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