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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) 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

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. It decomposes the total regret into counterfactual regrets, utilizing local regret minimization algorithms, such as…

Machine Learning · Computer Science 2024-05-15 Hang Xu , Kai Li , Bingyun Liu , Haobo Fu , Qiang Fu , Junliang Xing , Jian Cheng

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 (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

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 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 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

Counterfactual regret minimization is a family of algorithms of no-regret learning dynamics capable of solving large-scale imperfect information games. We propose implementing this algorithm as a series of dense and sparse matrix and vector…

Computer Science and Game Theory · Computer Science 2024-12-03 Juho Kim

Imperfect Information Games (IIGs) offer robust models for scenarios where decision-makers face uncertainty or lack complete information. Counterfactual Regret Minimization (CFR) has been one of the most successful family of algorithms for…

Machine Learning · Computer Science 2025-11-12 Jiayu Chen , Zhekai Wang , Vaneet Aggarwal

In many real-world scenarios, a team of agents coordinate with each other to compete against an opponent. The challenge of solving this type of game is that the team's joint action space grows exponentially with the number of agents, which…

Artificial Intelligence · Computer Science 2021-05-19 Shuxin Li , Youzhi Zhang , Xinrun Wang , Wanqi Xue , Bo An

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

Counterfactual Regret Minimization (CFR) is the most successful algorithm for finding approximate Nash equilibria in imperfect information games. However, CFR's reliance on full game-tree traversals limits its scalability. For this reason,…

Computer Science and Game Theory · Computer Science 2019-10-07 Eric Steinberger

Counterfactual Regret Minimization (CFR) is the most popular iterative algorithm for solving zero-sum imperfect-information games. Regret-Based Pruning (RBP) is an improvement that allows poorly-performing actions to be temporarily pruned,…

Computer Science and Game Theory · Computer Science 2016-09-13 Noam Brown , Tuomas Sandholm

Parallelization has played an instrumental role in the field of artificial intelligence (AI), drastically reducing the time taken to train and evaluate large AI models. In contrast to its impact in the broader field of AI, applying…

Artificial Intelligence · Computer Science 2026-05-15 Juho Kim , Tuomas Sandholm

The CFR+ algorithm for solving imperfect information games is a variant of the popular CFR algorithm, with faster empirical performance on a range of problems. It was introduced with a theoretical upper bound on solution error, but…

Computer Science and Game Theory · Computer Science 2019-02-21 Neil Burch , Matej Moravcik , Martin Schmid

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 (CFR) algorithms are a foundational class of methods for solving imperfect-information games, with the time average of their iterates converging to a Nash equilibrium in two-player zero-sum games. Prior…

Computer Science and Game Theory · Computer Science 2026-02-10 Naifeng Zhang , Stephen McAleer , Tuomas Sandholm
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