Deep Reinforcement Learning from Self-Play in Imperfect-Information Games (1603.01121v2)

Abstract: Many real-world applications can be described as large-scale games of imperfect information. To deal with these challenging domains, prior work has focused on computing Nash equilibria in a handcrafted abstraction of the domain. In this paper we introduce the first scalable end-to-end approach to learning approximate Nash equilibria without prior domain knowledge. Our method combines fictitious self-play with deep reinforcement learning. When applied to Leduc poker, Neural Fictitious Self-Play (NFSP) approached a Nash equilibrium, whereas common reinforcement learning methods diverged. In Limit Texas Holdem, a poker game of real-world scale, NFSP learnt a strategy that approached the performance of state-of-the-art, superhuman algorithms based on significant domain expertise.

• The paper introduces Neural Fictitious Self-Play (NFSP), combining reinforcement learning and self-play to autonomously approximate Nash equilibria in imperfect-information games.
• The method deploys dual neural networks—one for best-response learning and one for strategy averaging—enabling balanced exploration and exploitation without handcrafted abstractions.
• NFSP achieved competitive performance in Leduc Poker and Limit Texas Hold'em, indicating its scalability and potential for application in complex, real-world imperfect-information scenarios.

Deep Reinforcement Learning from Self-Play in Imperfect-Information Games

The paper by Heinrich and Silver presents a pioneering approach for learning approximate Nash equilibria in imperfect-information games using deep reinforcement learning (DRL) integrated with self-play. Traditional methods have relied heavily on handcrafted abstractions to compute Nash equilibria in these challenging domains, often involving significant human expertise and domain-specific knowledge. This work introduces Neural Fictitious Self-Play (NFSP), a scalable end-to-end approach that circumvents the need for prior knowledge, leveraging deep neural networks to autonomously learn effective strategies by simulating interactions through self-play.

Overview of the Approach

NFSP melds Fictitious Self-Play (FSP) with neural networks, allowing for the approximation of Nash equilibria without manual abstraction. FSP is an iterative method traditionally used in normal-form games to learn optimal strategies by averaging past actions to approximate opponents' behavior. In NFSP, two neural networks are deployed: one trained via reinforcement learning to predict action values and construct a best-response strategy; the other learns an average strategy through supervised learning, from memorized data of the agent's own behavior. This dual-network system allows agents to maintain a balance between exploring potential strategies and exploiting known high-value actions.

The method was evaluated in two domains: Leduc Poker, a simplified poker variant to test convergence to Nash equilibrium, and Limit Texas Hold'em (LHE), a full-scale poker game to assess performance relative to state-of-the-art strategies. NFSP agents demonstrated a marked ability to approach Nash equilibrium in Leduc poker, surpassing common RL methods. Notably, in LHE, the NFSP policy approximated the performance of top-tier algorithms developed with substantial domain expertise.

Implications and Contributions

NFSP's integration of deep RL with fictitious play represents a significant shift from traditional game-theoretic approaches, which typically require detailed game abstractions. The proposed technique's ability to learn directly from raw inputs via self-play offers several practical and theoretical implications:

1. Scalability and Generalizability: NFSP's architecture supports the scaling to more complex game settings, potentially expanding beyond traditional card or board games into real-world applications like negotiation or strategic planning, where the information is often incomplete and non-deterministic.
2. Automation of Strategy Derivation: By mitigating reliance on human-designed abstractions, NFSP reduces the human resource investment needed for strategy development, thus enabling broader experimentation across myriad domains.
3. Theoretical Contribution: The method showcases a novel use of neural networks in capturing and generalizing patterns from sequential decision processes in multi-agent settings, pushing the boundaries of deep learning applications in game theory.

Future Directions

While NFSP exhibits promise in strategic decision-making domains, future research may address several aspects to further enhance its applicability and robustness:

• Exploration of Continuous Action Spaces: Current implementation focuses on discrete actions; expanding to continuous action domains can broaden NFSP's usability in industrial applications requiring nuanced control strategies.
• Dynamic Multi-agent Environments: Extending NFSP to dynamically evolving environments where agents' strategies may change over time could improve adaptability and performance in real-time strategic applications.
• Integration with Other DRL Paradigms: Combining NFSP with methods like policy gradients or actor-critic models might enhance its convergence rate and stability in learning equilibria.

In summary, Heinrich and Silver's work on NFSP marks an important development in the field of AI and game theory, providing a foundation for further innovations in automated strategy learning in complex environments. The paper also opens up new avenues for exploration, potentially initiated by researchers aiming to deploy AI systems in imperfect-information settings without heavy dependence on pre-existing norms or complex abstractions.