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Monte Carlo Counterfactual Regret Minimization (MCCFR) has emerged as a cornerstone algorithm for solving extensive-form games, but its integration with deep neural networks introduces scale-dependent challenges that manifest differently…

Artificial Intelligence · Computer Science 2026-01-29 Zakaria El Jaafari

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

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

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

Learning strategies for imperfect information games from samples of interaction is a challenging problem. A common method for this setting, Monte Carlo Counterfactual Regret Minimization (MCCFR), can have slow long-term convergence rates…

Computer Science and Game Theory · Computer Science 2018-09-11 Martin Schmid , Neil Burch , Marc Lanctot , Matej Moravcik , Rudolf Kadlec , Michael Bowling

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

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

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

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

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) and its variants are widely recognized as effective algorithms for solving extensive-form imperfect information games. Recently, many improvements have been focused on enhancing the convergence speed…

Artificial Intelligence · Computer Science 2024-10-29 Ju Qi , Falin Hei , Ting Feng , Dengbing Yi , Zhemei Fang , Yunfeng Luo

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) 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

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

Online game playing algorithms produce high-quality strategies with a fraction of memory and computation required by their offline alternatives. Continual Resolving (CR) is a recent theoretically sound approach to online game playing that…

Computer Science and Game Theory · Computer Science 2019-03-11 Michal Sustr , Vojtech Kovarik , Viliam Lisy

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

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 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

Hindsight rationality is an approach to playing general-sum games that prescribes no-regret learning dynamics for individual agents with respect to a set of deviations, and further describes jointly rational behavior among multiple agents…

Computer Science and Game Theory · Computer Science 2022-06-03 Dustin Morrill , Ryan D'Orazio , Marc Lanctot , James R. Wright , Michael Bowling , Amy R. Greenwald

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
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