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Monte-Carlo counterfactual regret minimization (MCCFR) is the state-of-the-art algorithm for solving sequential games that are too large for full tree traversals. It works by using gradient estimates that can be computed via sampling.…

计算机科学与博弈论 · 计算机科学 2020-02-21 Gabriele Farina , Christian Kroer , Tuomas Sandholm

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…

人工智能 · 计算机科学 2024-10-29 Ju Qi , Falin Hei , Ting Feng , Dengbing Yi , Zhemei Fang , Yunfeng Luo

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…

计算机科学与博弈论 · 计算机科学 2019-03-11 Michal Sustr , Vojtech Kovarik , Viliam Lisy

This article discusses two contributions to decision-making in complex partially observable stochastic games. First, we apply two state-of-the-art search techniques that use Monte-Carlo sampling to the task of approximating a…

计算机科学与博弈论 · 计算机科学 2014-01-21 Marc Ponsen , Steven de Jong , Marc Lanctot

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,…

人工智能 · 计算机科学 2019-05-23 Noam Brown , Adam Lerer , Sam Gross , Tuomas Sandholm

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…

人工智能 · 计算机科学 2022-01-04 Huale Li , Xuan Wang , Zengyue Guo , Jiajia Zhang , Shuhan Qi

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…

机器学习 · 计算机科学 2025-11-12 Jiayu Chen , Zhekai Wang , Vaneet Aggarwal

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…

机器学习 · 计算机科学 2020-09-15 Huale Li , Xuan Wang , Fengwei Jia , Yifan Li , Yulin Wu , Jiajia Zhang , Shuhan Qi

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…

计算机科学与博弈论 · 计算机科学 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,…

机器学习 · 计算机科学 2025-11-12 Hang Xu , Kai Li , Haobo Fu , Qiang Fu , Junliang Xing , Jian Cheng

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,…

计算机科学与博弈论 · 计算机科学 2019-10-07 Eric Steinberger

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…

计算机科学与博弈论 · 计算机科学 2012-05-04 Marc Lanctot , Richard Gibson , Neil Burch , Martin Zinkevich , Michael Bowling

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…

人工智能 · 计算机科学 2018-12-31 Hui Li , Kailiang Hu , Zhibang Ge , Tao Jiang , Yuan Qi , Le Song

Counterfactual Regret Minimization (CFR) is the dominant algorithmic family for solving large imperfect-information games, underpinning breakthroughs such as Libratus and Pluribus in No-Limit Texas Hold'em poker. In real-time game-playing…

计算机科学与博弈论 · 计算机科学 2026-05-20 Boning Li , Longbo Huang

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)…

计算机科学与博弈论 · 计算机科学 2021-03-09 Gabriele Farina , Tuomas Sandholm

Regret minimization is a general approach to online optimization which plays a crucial role in many algorithms for approximating Nash equilibria in two-player zero-sum games. The literature mainly focuses on solving individual games in…

计算机科学与博弈论 · 计算机科学 2025-04-29 David Sychrovský , Martin Schmid , Michal Šustr , Michael Bowling

The Counterfactual Regret Minimization (CFR) algorithm and its variants have enabled the development of pokerbots capable of beating the best human players in heads-up (1v1) cash games and competing with them in six-player formats. However,…

机器学习 · 计算机科学 2026-02-24 Narada Maugin , Tristan Cazenave

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…

计算机科学与博弈论 · 计算机科学 2017-11-10 Gabriele Farina , Christian Kroer , Tuomas Sandholm

The literature on game-theoretic equilibrium finding predominantly focuses on single games or their repeated play. Nevertheless, numerous real-world scenarios feature playing a game sampled from a distribution of similar, but not identical…

计算机科学与博弈论 · 计算机科学 2024-02-21 David Sychrovský , Michal Šustr , Elnaz Davoodi , Michael Bowling , Marc Lanctot , Martin Schmid

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…

计算机科学与博弈论 · 计算机科学 2018-09-11 Gabriele Farina , Christian Kroer , Tuomas Sandholm
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