Counterfactual Regret Minimization (CFR) Algorithm

A Counterfactual Regret Minimization (CFR) Algorithm is a regret minimization algorithm that can be implemented by a counterfactual regret minimization system to solve a counterfactual regret minimization task (enables strategy optimization through regret-based learning).

• AKA: CFR Algorithm, CFR, Counterfactual Regret Minimization.
• Context:
  • Task Input: game description, player information
    • Optional Input: historical play data, domain constraints
  • Task Output: strategy profile, regret values
  • Task Performance Measure: convergence rate, exploitability, memory efficiency
  • ...
  • It can typically achieve Nash Equilibrium through iterative self-play.
  • It can typically minimize Regret Value through counterfactual value updating.
  • It can typically handle Imperfect Information through information set abstraction.
  • It can typically compute Strategy Profile through regret matching.
  • It can typically maintain Action Probability through strategy updating.
  • ...
  • It can often support Game Solving through recursive tree traversal.
  • It can often optimize Mixed Strategy through cumulative regret minimization.
  • It can often handle Partial Observability through sampling-based approximation.
  • It can often process Sequential Decision through history-aware computation.
  • ...
  • It can range from being a Vanilla CFR Implementation to being a Discounted CFR Implementation, depending on its update mechanism.
  • It can range from being a Table-Based CFR to being a Deep CFR, depending on its value representation.
  • ...
  • It can integrate with Neural Network for function approximation.
  • It can support Monte Carlo Sampling for performance optimization.
  • It can connect to Game Engine for strategy deployment.
  • ...
• Examples:
  • CFR Variants, such as:
    • Vanilla CFRs, such as:
      • External Sampling CFR for sampling-based computation.
      • Chance Sampling CFR for probability reduction.
    • Modern CFRs, such as:
      • Discounted CFR for faster convergence.
      • Linear CFR for improved stability.
  • CFR Applications, such as:
    • Game Solvers, such as:
      • Poker CFR System for poker strategy optimization.
      • Board Game CFR Engine for board game analysis.
    • Decision Systems, such as:
      • Security CFR System for defense strategy planning.
      • Trading CFR Engine for market strategy optimization.
  • ...
• Counter-Examples:
  • Policy Gradient Algorithm, which lacks counterfactual value computation.
  • Q-Learning Algorithm, which lacks explicit regret minimization.
  • Fictitious Play Algorithm, which lacks information set handling.
• See: Regret Minimization Algorithm, Counterfactual Regret Minimization System, Counterfactual Regret Minimization Task, Strategy Optimization, Regret-Based Learning, Game Theory Algorithm, Nash Equilibrium, Imperfect Information Game.

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References

2009

• (Lanctot et al., 2009) ⇒ Marc Lanctot, Kevin Waugh, Martin Zinkevich, and Michael Bowling. (2009). “Monte Carlo Sampling for Regret Minimization in Extensive Games.” In: Proceedings of the 22nd International Conference on Neural Information Processing Systems. ISBN:978-1-61567-911-9
  • QUOTE: Sequential decision-making with multiple agents and imperfect information is commonly modeled as an extensive game. One efficient method for computing Nash equilibria in large, zero-sum, imperfect information games is counterfactual regret minimization (CFR). In the domain of poker, CFR has proven effective, particularly when using a domain-specific augmentation involving chance outcome sampling. In this paper, we describe a general family of domain-independent CFR sample-based algorithms called Monte Carlo counterfactual regret minimization (MCCFR) of which the original and poker-specific versions are special cases.

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