Solving Large Imperfect Information Games Using CFR+
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Abstract (arXiv)
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 paper introduces CFR^+, a new algorithm that typically outperforms the previously known algorithms by an order of magnitude or more in terms of computation time while also potentially requiring less memory.
Key facts. Cited by 78 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Jul 2014.
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Citing papers per year: 2021: 9; 2022: 10; 2023: 14; 2024: 10; 2025: 15; 2026: 20.
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- 2023Language Agents with Reinforcement Learning for Strategic Play in the Werewolf Gamecited by 148
- 2023Suspicion-Agent: Playing Imperfect Information Games with Theory of Mind Aware GPT-4cited by 67
- 2022A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Gamescited by 64
- 2021XDO: A Double Oracle Algorithm for Extensive-Form Gamescited by 34
- 2023Multi-agent Reinforcement Learning: A Comprehensive Surveycited by 30
- 2021Last-iterate Convergence in Extensive-Form Gamescited by 27
- 2022Near-Optimal Learning of Extensive-Form Games with Imperfect Informationcited by 26
- 2024A Survey on Self-play Methods in Reinforcement Learningcited by 26
- 2021Simple Uncoupled No-Regret Learning Dynamics for Extensive-Form Correlated Equilibriumcited by 22
- 2021Model-Free Learning for Two-Player Zero-Sum Partially Observable Markov Games with Perfect Recallcited by 21
- 2021Efficient Deviation Types and Learning for Hindsight Rationality in Extensive-Form Gamescited by 14
- 2023Regret Matching+: (In)Stability and Fast Convergence in Gamescited by 13
38 more
- 2025Learning Strategic Language Agents in the Werewolf Game with Iterative Latent Space Policy Optimizationcited by 13
- 2025Reevaluating Policy Gradient Methods for Imperfect-Information Gamescited by 13
- 2021Model-Free Online Learning in Unknown Sequential Decision Making Problems and Gamescited by 12
- 2022Adapting to game trees in zero-sum imperfect information gamescited by 11
- 2024RL-CFR: Improving Action Abstraction for Imperfect Information Extensive-Form Games with Reinforcement Learningcited by 10
- 2023Adaptively Perturbed Mirror Descent for Learning in Gamescited by 9
- 2021Search in Imperfect Information Gamescited by 8
- 2022Mutation-Driven Follow the Regularized Leader for Last-Iterate Convergence in Zero-Sum Gamescited by 8
- 2022HSVI can solve zero-sum Partially Observable Stochastic Gamescited by 8
- 2024Minimizing Weighted Counterfactual Regret with Optimistic Online Mirror Descentcited by 7
- 2026How Far Are LLMs from Professional Poker Players? Revisiting Game-Theoretic Reasoning with Agentic Tool Usecited by 7
- 2022A Marriage between Adversarial Team Games and 2-player Games: Enabling Abstractions, No-regret Learning, and Subgame Solvingcited by 6
- 2025From Average-Iterate to Last-Iterate Convergence in Games: A Reduction and Its Applicationscited by 6
- 2026Real-Time Parallel Counterfactual Regret Minimizationcited by 6
- 2023Last-Iterate Convergence Properties of Regret-Matching Algorithms in Gamescited by 5
- 2022Public Information Representation for Adversarial Team Gamescited by 4
- 2022Learning Correlated Equilibria in Mean-Field Gamescited by 4
- 2026Agents That Certify Their Own Exploits: Confidence-Scheduled Restricted Responses for Safe Opponent Exploitationcited by 4
- 2021Optimistic and Adaptive Lagrangian Hedgingcited by 3
- 2022A Survey of Decision Making in Adversarial Gamescited by 3
- 2023Guarantees for Self-Play in Multiplayer Games via Polymatrix Decomposabilitycited by 3
- 2025Scale-Invariant Regret Matching and Online Learning with Optimal Convergence: Bridging Theory and Practice in Zero-Sum Gamescited by 3
- 2026Discovering Multiagent Learning Algorithms with Large Language Modelscited by 3
- 2026When a Verified World Model Still Loses: Play-Adequacy vs Prediction-Accuracy in LLM-Synthesized Code World Modelscited by 3
- 2023Learning not to Regretcited by 2
- 2023Local and adaptive mirror descents in extensive-form gamescited by 2
- 2024Understanding Iterative Combinatorial Auction Designs via Multi-Agent Reinforcement Learningcited by 2
- 2025Convergence of Regret Matching in Potential Games and Constrained Optimizationcited by 2
- 2026Code-Space Response Oracles: Generating Interpretable Multi-Agent Policies with Large Language Modelscited by 2
- 2026Parallelizing Counterfactual Regret Minimizationcited by 2
- 2026Which Nash Equilibrium? Solver-Dependent Selection on Zero-Sum Nash Polytopescited by 2
- 2026Optimal Alternating Regret for Online Learning and Gamescited by 2
- 2023Composing Efficient, Robust Tests for Policy Selectioncited by 1
- 2024Balancing the AI Strength of Roles in Self-Play Training with Regret Matching+cited by 1
- 2024Optimistic Thompson Sampling for No-Regret Learning in Unknown Gamescited by 1
- 2024Configurable Mirror Descent: Towards a Unification of Decision Makingcited by 1
- 2025On the Power of Perturbation under Sampling in Solving Extensive-Form Gamescited by 1
- 2025Faster Game Solving via Asymmetry of Step Sizescited by 1
50 most cited of 78 All 78 (JSON)
- 2026Steering Equilibrium Selection in Regularized Self-Play via the Reference Policy17 Sep 2026
- 2026GPU-CFR: 80x Faster Counterfactual Regret Minimization by Compiling the Game to Static Dataflow and CUDA Graph Replay10 Sep 2026
- 2026Minimax Alternating Regret for the Experts Problem and Online Convex Optimization25 Aug 2026
- 2026Optimal Alternating Regret for Online Learning and Games25 Aug 2026
- 2026CFR without Unbiasedness: Deterministic Guarantees for Persistent Public-Chance Schedules14 Aug 2026
- 2026AV-AIVAT: 74x Cheaper Agent Evaluation with Certified Anytime-Valid Stopping in Imperfect-Information Games6 Aug 2026
- 2026Agents That Certify Their Own Exploits: Confidence-Scheduled Restricted Responses for Safe Opponent Exploitation30 Jul 2026
- 2026Distributed Constraint Optimization via Online Learning and Iterative Pricing with Application to Large-Scale Satellite Scheduling28 Jul 2026
- 2026LeAct: Learning to Reason from Expert Actions23 Jul 2026
- 2026When a Verified World Model Still Loses: Play-Adequacy vs Prediction-Accuracy in LLM-Synthesized Code World Models15 Jul 2026
- 2026Coachable agents for interactive gameplay1 Jul 2026
- 2026Which Nash Equilibrium? Solver-Dependent Selection on Zero-Sum Nash Polytopes26 Jun 2026
38 more
- 2026GENSTRAT: Toward a Science of Strategic Reasoning in Large Language Models22 May 2026
- 2026Real-Time Parallel Counterfactual Regret Minimization19 May 2026
- 2026Parallelizing Counterfactual Regret Minimization14 May 2026
- 2026On-line Learning in Tree MDPs by Treating Policies as Bandit Arms6 May 2026
- 2026Code-Space Response Oracles: Generating Interpretable Multi-Agent Policies with Large Language Models10 Mar 2026
- 2026NePPO: Near-Potential Policy Optimization for General-Sum Multi-Agent Reinforcement Learning7 Mar 2026
- 2026Discovering Multiagent Learning Algorithms with Large Language Models18 Feb 2026
- 2026How Far Are LLMs from Professional Poker Players? Revisiting Game-Theoretic Reasoning with Agentic Tool Use31 Jan 2026
- 2025Deep (Predictive) Discounted Counterfactual Regret Minimization11 Nov 2025
- 2025Convergence of Regret Matching in Potential Games and Constrained Optimization20 Oct 2025
- 2025Beyond Outcome-Based Imperfect-Recall: Higher-Resolution Abstractions for Imperfect-Information Games16 Oct 2025
- 2025Look-ahead Reasoning with a Learned Model in Imperfect Information Games6 Oct 2025
- 2025Scale-Invariant Regret Matching and Online Learning with Optimal Convergence: Bridging Theory and Practice in Zero-Sum Games6 Oct 2025
- 2025Beyond Game Theory Optimal: Profit-Maximizing Poker Agents for No-Limit Holdem28 Sep 2025
- 2025Efficient Last-Iterate Convergence in Regret Minimization via Adaptive Reward Transformation17 Sep 2025
- 2025Solving Pasur Using GPU-Accelerated Counterfactual Regret Minimization6 Aug 2025
- 2025From Average-Iterate to Last-Iterate Convergence in Games: A Reduction and Its Applications4 Jun 2025
- 2025Meta-Learning in Self-Play Regret Minimization26 Apr 2025
- 2025Approximating Nash Equilibria in General-Sum Games via Meta-Learning26 Apr 2025
- 2025Faster Game Solving via Asymmetry of Step Sizes17 Mar 2025
- 2025Reevaluating Policy Gradient Methods for Imperfect-Information Games13 Feb 2025
- 2025Learning Strategic Language Agents in the Werewolf Game with Iterative Latent Space Policy Optimization7 Feb 2025
- 2025On the Power of Perturbation under Sampling in Solving Extensive-Form Games28 Jan 2025
- 2024GPU-Accelerated Counterfactual Regret Minimization27 Aug 2024
- 2024A Survey on Self-play Methods in Reinforcement Learning2 Aug 2024
- 2024ε-Optimally Solving Zero-Sum POSGs29 May 2024
- 2024Configurable Mirror Descent: Towards a Unification of Decision Making20 May 2024
- 2024Minimizing Weighted Counterfactual Regret with Optimistic Online Mirror Descent22 Apr 2024
- 2024RL-CFR: Improving Action Abstraction for Imperfect Information Extensive-Form Games with Reinforcement Learning7 Mar 2024
- 2024Understanding Iterative Combinatorial Auction Designs via Multi-Agent Reinforcement Learning29 Feb 2024
- 2024Easy as ABCs: Unifying Boltzmann Q-Learning and Counterfactual Regret Minimization19 Feb 2024
- 2024Optimistic Thompson Sampling for No-Regret Learning in Unknown Games7 Feb 2024
- 2024Balancing the AI Strength of Roles in Self-Play Training with Regret Matching+23 Jan 2024
- 2023Multi-agent Reinforcement Learning: A Comprehensive Survey15 Dec 2023
- 2023Last-Iterate Convergence Properties of Regret-Matching Algorithms in Games1 Nov 2023
- 2023Language Agents with Reinforcement Learning for Strategic Play in the Werewolf Game29 Oct 2023
- 2023Guarantees for Self-Play in Multiplayer Games via Polymatrix Decomposability17 Oct 2023
- 2023A Generalized Extensive-Form Fictitious Play Algorithm14 Oct 2023
50 newest of 78 All 78 (JSON)
- 2023Language Agents with Reinforcement Learning for Strategic Play in the Werewolf Gamecited by 148
- 2023Suspicion-Agent: Playing Imperfect Information Games with Theory of Mind Aware GPT-4cited by 67
- 2025Learning Strategic Language Agents in the Werewolf Game with Iterative Latent Space Policy Optimizationcited by 13
- 2026Code-Space Response Oracles: Generating Interpretable Multi-Agent Policies with Large Language Modelscited by 2
- 2026AV-AIVAT: 74x Cheaper Agent Evaluation with Certified Anytime-Valid Stopping in Imperfect-Information Gamescited by 1
- 2026Coachable agents for interactive gameplaycited by 0
- 2026AV-AIVAT: 74x Cheaper Agent Evaluation with Certified Anytime-Valid Stopping in Imperfect-Information Games6 Aug 2026
- 2026Coachable agents for interactive gameplay1 Jul 2026
- 2026Code-Space Response Oracles: Generating Interpretable Multi-Agent Policies with Large Language Models10 Mar 2026
- 2025Learning Strategic Language Agents in the Werewolf Game with Iterative Latent Space Policy Optimization7 Feb 2025
- 2023Language Agents with Reinforcement Learning for Strategic Play in the Werewolf Game29 Oct 2023
- 2023Suspicion-Agent: Playing Imperfect Information Games with Theory of Mind Aware GPT-429 Sep 2023
- 2026How Far Are LLMs from Professional Poker Players? Revisiting Game-Theoretic Reasoning with Agentic Tool Usecited by 7
- 2025Look-ahead Reasoning with a Learned Model in Imperfect Information Gamescited by 1
- 2026GENSTRAT: Toward a Science of Strategic Reasoning in Large Language Modelscited by 0
- 2026LeAct: Learning to Reason from Expert Actionscited by 0
- 2026LeAct: Learning to Reason from Expert Actions23 Jul 2026
- 2026GENSTRAT: Toward a Science of Strategic Reasoning in Large Language Models22 May 2026
- 2026How Far Are LLMs from Professional Poker Players? Revisiting Game-Theoretic Reasoning with Agentic Tool Use31 Jan 2026
- 2025Look-ahead Reasoning with a Learned Model in Imperfect Information Games6 Oct 2025
- 2022A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Gamescited by 64
- 2021XDO: A Double Oracle Algorithm for Extensive-Form Gamescited by 34
- 2023Multi-agent Reinforcement Learning: A Comprehensive Surveycited by 30
- 2021Last-iterate Convergence in Extensive-Form Gamescited by 27
- 2022Near-Optimal Learning of Extensive-Form Games with Imperfect Informationcited by 26
- 2024A Survey on Self-play Methods in Reinforcement Learningcited by 26
- 2021Simple Uncoupled No-Regret Learning Dynamics for Extensive-Form Correlated Equilibriumcited by 22
- 2021Model-Free Learning for Two-Player Zero-Sum Partially Observable Markov Games with Perfect Recallcited by 21
- 2021Efficient Deviation Types and Learning for Hindsight Rationality in Extensive-Form Gamescited by 14
- 2023Regret Matching+: (In)Stability and Fast Convergence in Gamescited by 13
- 2025Reevaluating Policy Gradient Methods for Imperfect-Information Gamescited by 13
- 2021Model-Free Online Learning in Unknown Sequential Decision Making Problems and Gamescited by 12
12 most cited of 67 All 67 (JSON)
- 2026Steering Equilibrium Selection in Regularized Self-Play via the Reference Policy17 Sep 2026
- 2026GPU-CFR: 80x Faster Counterfactual Regret Minimization by Compiling the Game to Static Dataflow and CUDA Graph Replay10 Sep 2026
- 2026Minimax Alternating Regret for the Experts Problem and Online Convex Optimization25 Aug 2026
- 2026Optimal Alternating Regret for Online Learning and Games25 Aug 2026
- 2026CFR without Unbiasedness: Deterministic Guarantees for Persistent Public-Chance Schedules14 Aug 2026
- 2026Agents That Certify Their Own Exploits: Confidence-Scheduled Restricted Responses for Safe Opponent Exploitation30 Jul 2026
- 2026Distributed Constraint Optimization via Online Learning and Iterative Pricing with Application to Large-Scale Satellite Scheduling28 Jul 2026
- 2026Which Nash Equilibrium? Solver-Dependent Selection on Zero-Sum Nash Polytopes26 Jun 2026
- 2026Real-Time Parallel Counterfactual Regret Minimization19 May 2026
- 2026Parallelizing Counterfactual Regret Minimization14 May 2026
- 2026On-line Learning in Tree MDPs by Treating Policies as Bandit Arms6 May 2026
- 2026NePPO: Near-Potential Policy Optimization for General-Sum Multi-Agent Reinforcement Learning7 Mar 2026
12 newest of 67 All 67 (JSON)