Counterfactual Regret Minimization (CFR) is the most successful algorithm for finding approximate Nash equilibria in imperfect information games. However, CFR's reliance on full game-tree traversals limits its scalability. For this reason, the game's state- and action-space is often abstracted (i.e. simplified) for CFR, and the resulting strategy is then translated back to the full game, which requires extensive expert-knowledge and often converges to highly exploitable policies. A recently proposed method, Deep CFR, applies deep learning directly to CFR, allowing the agent to intrinsically abstract and generalize over the state-space from samples, without requiring expert knowledge. In this paper, we introduce Single Deep CFR (SD-CFR), a simplified variant of Deep CFR that has a lower overall approximation error by avoiding the training of an average strategy network. We show that SD-CFR is more attractive from a theoretical perspective and empirically outperforms Deep CFR with respect to exploitability and one-on-one play in poker.
A very successful application of deep learning to CFR in the domain of poker is @cite_4 , an algorithm that was able to defeat professional poker players in head-to-head gameplay in the game of Heads-Up No-Limit Hold'em Poker (HUNL) with statistical significance. However, while DeepStack works very well in poker, it still relies on tabular CFR methods to generate data for its counterfactual value networks and for re-solving. This could be too expensive in environments, where sample complexity is a concern. Furthermore, because DeepStack does not use any card abstraction, it would have difficulties handling games with many more private information states than HUNL has.
@cite_4
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Artificial intelligence has seen several breakthroughs in recent years, with games often serving as milestones. A common feature of these games is that players have perfect information. Poker, the quintessential game of imperfect information, is a long-standing challenge problem in artificial intelligence. We introduce DeepStack, an algorithm for imperfect-information settings. It combines recursive reasoning to handle information asymmetry, decomposition to focus computation on the relevant decision, and a form of intuition that is automatically learned from self-play using deep learning. In a study involving 44,000 hands of poker, DeepStack defeated, with statistical significance, professional poker players in heads-up no-limit Texas hold’em. The approach is theoretically sound and is shown to produce strategies that are more difficult to exploit than prior approaches. In two-player zero-sum games, if both players minimize their average external regret, then the average of the strategy profiles converges to a Nash equilibrium. For n-player general-sum games, however, theoretical guarantees for regret minimization are less understood. Nonetheless, Counterfactual Regret Minimization (CFR), a popular regret minimization algorithm for extensive-form games, has generated winning three-player Texas Hold'em agents in the Annual Computer Poker Competition (ACPC). In this paper, we provide the first set of theoretical properties for regret minimization algorithms in non-zero-sum games by proving that solutions eliminate iterative strict domination. We formally define in extensive-form games, show that CFR avoids iteratively strictly dominated actions and strategies, and demonstrate that removing iteratively dominated actions is enough to win a mock tournament in a small poker game. In addition, for two-player non-zero-sum games, we bound the worst case performance and show that in practice, regret minimization can yield strategies very close to equilibrium. Our theoretical advancements lead us to a new modification of CFR for games with more than two players that is more efficient and may be used to generate stronger strategies than previously possible. Furthermore, we present a new three-player Texas Hold'em poker agent that was built using CFR and a novel game decomposition method. Our new agent wins the three-player events of the 2012 ACPC and defeats the winning three-player programs from previous competitions while requiring less resources to generate than the 2011 winner. Finally, we show that our CFR modification computes a strategy of equal quality to our new agent in a quarter of the time of standard CFR using half the memory. Games are used to evaluate and advance Multiagent and Artificial Intelligence techniques. Most of these games are deterministic with perfect information (e.g. Chess and Checkers). A deterministic game has no chance element and in a perfect information game, all information is visible to all players. However, many real-world scenarios with competing agents are stochastic (non-deterministic) with imperfect information. For two-player zero-sum perfect recall games, a recent technique called Counterfactual Regret Minimization (CFR) computes strategies that are provably convergent to an e-Nash equilibrium. A Nash equilibrium strategy is useful in two-player games since it maximizes its utility against a worst-case opponent. However, for multiplayer (three or more player) games, we lose all theoretical guarantees for CFR. However, we believe that CFR-generated agents may perform well in multiplayer games. To test this hypothesis, we used this technique to create several 3-player limit Texas Hold'em poker agents and two of them placed first and second in the 3-player event of the 2009 AAAI IJCAI Computer Poker Competition. We also demonstrate that good strategies can be obtained by grafting sets of two-player subgame strategies to a 3-player base strategy after one of the players is eliminated. Recently, very deep convolutional neural networks (CNNs) have shown outstanding performance in object recognition and have also been the first choice for dense classification problems such as semantic segmentation. However, repeated subsampling operations like pooling or convolution striding in deep CNNs lead to a significant decrease in the initial image resolution. Here, we present RefineNet, a generic multi-path refinement network that explicitly exploits all the information available along the down-sampling process to enable high-resolution prediction using long-range residual connections. In this way, the deeper layers that capture high-level semantic features can be directly refined using fine-grained features from earlier convolutions. The individual components of RefineNet employ residual connections following the identity mapping mindset, which allows for effective end-to-end training. Further, we introduce chained residual pooling, which captures rich background context in an efficient manner. We carry out comprehensive experiments and set new state-of-the-art results on seven public datasets. In particular, we achieve an intersection-over-union score of 83.4 on the challenging PASCAL VOC 2012 dataset, which is the best reported result to date.