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Optimization of deep learning algorithms to approach Nash Equilibrium remains a significant problem in imperfect information games, e.g. StarCraft and poker. Neural Fictitious Self-Play (NFSP) has provided an effective way to learn…

Artificial Intelligence · Computer Science 2021-04-23 Yuxuan Chen , Li Zhang , Shijian Li , Gang Pan

Computational equilibrium finding in large zero-sum extensive-form imperfect-information games has led to significant recent AI breakthroughs. The fastest algorithms for the problem are new forms of counterfactual regret minimization [Brown…

Computer Science and Game Theory · Computer Science 2020-07-01 Brian Hu Zhang , 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

There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer strategic-form games. While…

Computer Science and Game Theory · Computer Science 2025-10-01 Sam Ganzfried

High-quality information set abstraction remains a core challenge in solving large-scale imperfect-information extensive-form games (IIEFGs)--such as no-limit Texas Hold'em--where the finite nature of spatial resources hinders solving…

Artificial Intelligence · Computer Science 2025-12-10 Yanchang Fu , Shengda Liu , Pei Xu , Kaiqi Huang

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

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,…

Machine Learning · Computer Science 2026-02-24 Narada Maugin , Tristan Cazenave

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 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…

Computer Science and Game Theory · Computer Science 2026-05-20 Boning Li , Longbo Huang

Extensive-form games (EFGs) model finite sequential interactions between players. The amount of memory required to represent these games is the main bottleneck of algorithms for computing optimal strategies and the size of these strategies…

Computer Science and Game Theory · Computer Science 2020-04-16 Jiri Cermak , Viliam Lisy , Branislav Bosansky

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 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

Extensive-form games are a common model for multiagent interactions with imperfect information. In two-player zero-sum games, the typical solution concept is a Nash equilibrium over the unconstrained strategy set for each player. In many…

Computer Science and Game Theory · Computer Science 2019-02-07 Trevor Davis , Kevin Waugh , Michael Bowling

There has been tremendous recent progress on equilibrium-finding algorithms for zero-sum imperfect-information extensive-form games, but there has been a puzzling gap between theory and practice. First-order methods have significantly…

Computer Science and Game Theory · Computer Science 2018-10-09 Christian Kroer , Gabriele Farina , 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

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

Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has…

Computer Science and Game Theory · Computer Science 2021-02-19 Sam Ganzfried

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

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…

Computer Science and Game Theory · Computer Science 2014-01-21 Marc Ponsen , Steven de Jong , Marc Lanctot

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