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Solving Imperfect-Information Games via Discounted Regret Minimization

arXiv 1809.04040 ↗First posted 11 Sep 2018cs.GT cs.AIcited by 68

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Abstract (arXiv)

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 variants that 1) discount regrets from earlier iterations in various ways (in some cases differently for positive and negative regrets), 2) reweight iterations in various ways to obtain the output strategies, 3) use a non-standard regret minimizer and/or 4) leverage "optimistic regret matching". They lead to dramatically improved performance in many settings. For one, we introduce a variant that outperforms CFR+, the prior state-of-the-art algorithm, in every game tested, including large-scale realistic settings. CFR+ is a formidable benchmark: no other algorithm has been able to outperform it. Finally, we show that, unlike CFR+, many of the important new variants are compatible with modern imperfect-information-game pruning techniques and one is also compatible with sampling in the game tree.

Key facts. Cited by 68 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Sep 2018.

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Citing papers per year: 2021: 13; 2022: 9; 2023: 7; 2024: 12; 2025: 17; 2026: 10.

68 papers.

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  1. 2021DouZero: Mastering DouDizhu with Self-Play Deep Reinforcement Learningcited by 65
  2. 2021No-Press Diplomacy from Scratchcited by 31
  3. 2021Last-iterate Convergence in Extensive-Form Gamescited by 27
  4. 2024A Survey on Self-play Methods in Reinforcement Learningcited by 26
  5. 2021Simple Uncoupled No-Regret Learning Dynamics for Extensive-Form Correlated Equilibriumcited by 22
  6. 2022The Power of Regularization in Solving Extensive-Form Gamescited by 21
  7. 2024PokerGPT: An End-to-End Lightweight Solver for Multi-Player Texas Hold'em via Large Language Modelcited by 20
  8. 2021Provably Efficient Policy Optimization for Two-Player Zero-Sum Markov Gamescited by 18
  9. 2021Bandit Linear Optimization for Sequential Decision Making and Extensive-Form Gamescited by 15
  10. 2023On the Convergence of No-Regret Learning Dynamics in Time-Varying Gamescited by 14
  11. 2021Better Regularization for Sequential Decision Spaces: Fast Convergence Rates for Nash, Correlated, and Team Equilibriacited by 13
  12. 2025Reevaluating Policy Gradient Methods for Imperfect-Information Gamescited by 13
38 more
  1. 2021Model-Free Online Learning in Unknown Sequential Decision Making Problems and Gamescited by 12
  2. 2024Discounted Adaptive Online Learning: Towards Better Regularizationcited by 12
  3. 2024RL-CFR: Improving Action Abstraction for Imperfect Information Extensive-Form Games with Reinforcement Learningcited by 10
  4. 2022Anytime PSRO for Two-Player Zero-Sum Gamescited by 9
  5. 2022Mutation-Driven Follow the Regularized Leader for Last-Iterate Convergence in Zero-Sum Gamescited by 8
  6. 2021Equivalence Analysis between Counterfactual Regret Minimization and Online Mirror Descentcited by 7
  7. 2024Minimizing Weighted Counterfactual Regret with Optimistic Online Mirror Descentcited by 7
  8. 2026Real-Time Parallel Counterfactual Regret Minimizationcited by 6
  9. 2024A Policy-Gradient Approach to Solving Imperfect-Information Games with Best-Iterate Convergencecited by 5
  10. 2026PokerSkill: LLMs Can Play Expert-Level Poker without Training or Solverscited by 5
  11. 2021CFR-MIX: Solving Imperfect Information Extensive-Form Games with Combinatorial Action Spacecited by 4
  12. 2022Public Information Representation for Adversarial Team Gamescited by 4
  13. 2022Solving optimization problems with Blackwell approachabilitycited by 4
  14. 2026Agents That Certify Their Own Exploits: Confidence-Scheduled Restricted Responses for Safe Opponent Exploitationcited by 4
  15. 2022A Survey of Decision Making in Adversarial Gamescited by 3
  16. 2024LiteEFG: An Efficient Python Library for Solving Extensive-form Gamescited by 3
  17. 2025Scale-Invariant Regret Matching and Online Learning with Optimal Convergence: Bridging Theory and Practice in Zero-Sum Gamescited by 3
  18. 2026Discovering Multiagent Learning Algorithms with Large Language Modelscited by 3
  19. 2022Offline Equilibrium Findingcited by 2
  20. 2023Learning not to Regretcited by 2
  21. 2024Understanding Iterative Combinatorial Auction Designs via Multi-Agent Reinforcement Learningcited by 2
  22. 2024On the Optimality of Dilated Entropy and Lower Bounds for Online Learning in Extensive-Form Gamescited by 2
  23. 2025Discounted Online Convex Optimization: Uniform Regret Across a Continuous Intervalcited by 2
  24. 2025Convergence of Regret Matching in Potential Games and Constrained Optimizationcited by 2
  25. 2026Parallelizing Counterfactual Regret Minimizationcited by 2
  26. 2026Solver-Guided Reasoning for Mixed-Equilibrium Strategiescited by 2
  27. 2022Generalized Bandit Regret Minimizer Framework in Imperfect Information Extensive-Form Gamecited by 1
  28. 2025On the Power of Perturbation under Sampling in Solving Extensive-Form Gamescited by 1
  29. 2025Faster Game Solving via Asymmetry of Step Sizescited by 1
  30. 2025Approximating Nash Equilibria in General-Sum Games via Meta-Learningcited by 1
  31. 2025Solving Pasur Using GPU-Accelerated Counterfactual Regret Minimizationcited by 1
  32. 2025Beyond Outcome-Based Imperfect-Recall: Higher-Resolution Abstractions for Imperfect-Information Gamescited by 1
  33. 2025Deep (Predictive) Discounted Counterfactual Regret Minimizationcited by 1
  34. 2026AV-AIVAT: 74x Cheaper Agent Evaluation with Certified Anytime-Valid Stopping in Imperfect-Information Gamescited by 1
  35. 2021ScrofaZero: Mastering Trick-taking Poker Game Gongzhu by Deep Reinforcement Learningcited by 0
  36. 2021Uncoupled Bandit Learning towards Rationalizability: Benchmarks, Barriers, and Algorithmscited by 0
  37. 2021Revisiting Game Representations: The Hidden Costs of Efficiency in Sequential Decision-making Algorithmscited by 0
  38. 2022DecisionHoldem: Safe Depth-Limited Solving With Diverse Opponents for Imperfect-Information Gamescited by 0

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