Deep Counterfactual Regret Minimization (1811.00164v3)

Abstract: 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, abstraction is typically applied before running CFR. The abstracted game is solved with tabular CFR, and its solution is mapped back to the full game. This process can be problematic because aspects of abstraction are often manual and domain specific, abstraction algorithms may miss important strategic nuances of the game, and there is a chicken-and-egg problem because determining a good abstraction requires knowledge of the equilibrium of the game. This paper introduces Deep Counterfactual Regret Minimization, a form of CFR that obviates the need for abstraction by instead using deep neural networks to approximate the behavior of CFR in the full game. We show that Deep CFR is principled and achieves strong performance in large poker games. This is the first non-tabular variant of CFR to be successful in large games.

• The paper introduces Deep CFR, a method that integrates deep neural networks with traditional CFR to eliminate the need for game abstractions in imperfect-information games.
• It employs dual networks to approximate regret and strategy profiles, leveraging Monte Carlo sampling to ensure balanced exploration.
• Empirical results in heads-up poker demonstrate that Deep CFR achieves lower exploitability and faster convergence compared to prior abstraction-based methods.

Deep Counterfactual Regret Minimization

The paper "Deep Counterfactual Regret Minimization" advances the paper of algorithms for solving extensive-form games with imperfect information by introducing a novel approach that integrates Counterfactual Regret Minimization (CFR) with deep neural networks. This integration is significant because it addresses the limitations of traditional CFR methods, which require abstraction of the game to manage large state spaces.

Conceptual Outline

Counterfactual Regret Minimization is central to solving imperfect-information games by iteratively learning the player's strategy and aiming to converge to a Nash equilibrium. Traditional CFR methods use tabular representations for strategy and regret calculations, which become computationally expensive and impractical for large games. Abstractions are used to simplify game states, but this introduces inaccuracies and dependency on domain knowledge. Deep CFR eliminates the need for these abstractions by employing neural networks to learn directly from the full game state space, approximating the tabular CFR's regret and strategy profiles.

Methodological Advances

Deep CFR merges deep learning with game-theoretic algorithms, leveraging neural networks to approximate expected counterfactual regrets. The method utilizes an architecture that consists of two separate networks: one for predicting action advantage values (regrets) and another for the average strategy over iterations. These networks are trained from experiences generated via Monte Carlo samples of game traversals, thus balancing exploration and empirically-grounded learning.

One of the critical achievements of this method is its ability to handle large imperfect-information games like poker, without relying heavily on abstraction techniques. It provides systematic training of neural networks that approximate the complex functions required for CFR, aligning well with the principles of regret minimization and strategy learning in extensive-form games.

Empirical Results

Evaluations were conducted in heads-up poker variants, including heads-up limit Texas hold'em and flop hold'em poker. The Deep CFR algorithm was compared against Neural Fictitious Self Play (NFSP) and demonstrated superior convergence rates and lower exploitability in terms of milli big blinds per game (mbb/g) metric. Deep CFR achieved strong performance relative to domain-specific abstraction techniques, reaching levels of exploitability comparable to advanced abstraction approaches with reduced computational reliance.

Theoretical and Practical Implications

The theoretical soundness of Deep CFR is supported through convergence proofs that bound the algorithm's average regret concerning function approximation errors. This paper suggests that deep learning frameworks can robustly generalize over large and complex strategic spaces-theoretically contributing to multi-agent learning paradigms.

Practically, Deep CFR has implications for developing AI agents capable of complex strategic decision-making in vast informational landscapes without formal abstractions, paving the way for applications beyond traditional gaming. This flexibility is crucial for domains where abstraction knowledge is limited or disproportionately expensive to generate.

Future Developments

Deep CFR opens possibilities for future research directions, particularly in enhancing the scalability of sampling methods within even larger games and improving variance reduction techniques to ensure stable learning and convergence. Additional work may focus on extending the algorithm to accommodate more players, non-zero-sum dynamics, or applying to other strategic domains like economic modeling and cybersecurity.

In conclusion, Deep Counterfactual Regret Minimization is a compelling advancement that integrates cutting-edge deep learning techniques with classical game theory, offering a powerful tool for solving large-scale imperfect-information games without reliance on abstraction.