Player of Games

Schmid, Martin; Moravčík, Matej; Burch, Neil; Kadlec, Rudolf; Davidson, Josh; Waugh, Kevin; Bard, Nolan; Timbers, Finbarr; Lanctot, Marc; Holland, Zach; Davoodi, Elnaz; Christianson, Alden; Bowling, Michael

doi:10.48550/arxiv.2112.03178

Cited by 13 publications

(19 citation statements)

References 29 publications

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“…Nonetheless, they form a closed system where, in theory, every combination of card shuffle and every possible bid could be simulated with exhaustive search and have regularities that could be exploited probabilistically using methods similar to the preceding methods. Google's PoG (Player of Games) already plays high-level poker [29], and at this writing, NukkAI has defeated eight world bridge champions [30,31].…”

Section: Probabilistic Searchmentioning

confidence: 99%

The Accidental Philosopher and One of the Hardest Problems in the World

Finnestad

Neufeld²

2022

Philosophies

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Given the difficulties of defining “machine” and “think”, Turing proposed to replace the question “Can machines think?” with a proxy: how well can an agent engage in sustained conversation with a human? Though Turing neither described himself as a philosopher nor published much on philosophical matters, his Imitation Game has stood the test of time. Most understood at that time that success would not come easy, but few would have guessed just how difficult engaging in ordinary conversation would turn out to be. Despite the proliferation of language processing tools, we have seen little progress towards doing well at the Imitation Game. Had Turing instead suggested ability at games or even translation as a proxy for intelligence, his paper might have been forgotten. We argue that these and related problems are amenable to mechanical, though sophisticated, formal techniques. Turing appears to have taken care to select sustained, productive conversation and that alone as his proxy. Even simple conversation challenges a machine to engage in the rich practice of human discourse in all its generality and variety.

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Section: Probabilistic Searchmentioning

confidence: 99%

The Accidental Philosopher and One of the Hardest Problems in the World

Finnestad

Neufeld²

2022

Philosophies

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“…Some previous works explicitly discuss and exploit the simplifying properties of poker [9,14,10]. Similarly, the recent paper [20] acknowledges its use of a very specific version of the counterfactual regret minimization algorithm (CFR), though it does not go into details regarding the differences between this version and the vanilla CFR [27]. However, a vast majority of recent papers present their analysis for EFGs but only implement (and evaluate) their ideas on poker or games with nearidentical structure (such as liar's dice).…”

Section: Introductionmentioning

confidence: 99%

Fast Algorithms for Poker Require Modelling it as a Sequential Bayesian Game

Kovařík¹,

Milec²,

Šustr³

et al. 2021

Preprint

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Many recent results in imperfect information games were only formulated for, or evaluated on, poker and poker-like games such as liar's dice. We argue that sequential Bayesian games constitute a natural class of games for generalizing these results. In particular, this model allows for an elegant formulation of the counterfactual regret minimization algorithm, called publicstate CFR (PS-CFR), which naturally lends itself to an efficient implementation. Empirically, solving a poker subgame with 10 7 states by public-state CFR takes 3 minutes and 700 MB while a comparable version of vanilla CFR takes 5.5 hours and 20 GB. Additionally, the public-state formulation of CFR opens up the possibility for exploiting domain-specific assumptions, leading to a quadratic reduction in asymptotic complexity (and a further empirical speedup) over vanilla CFR in poker and other domains. Overall, this suggests that the ability to represent poker as a Bayesian extensive game played a key role in the success of CFR-based methods. Finally, we extend public-state CFR to general extensive-form games, arguing that this extension enjoys some -but not all -of the benefits of the version for sequential Bayesian games.

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“…This paper is concerned with the problem of learning equilibria in Imperfect-Information Extensive-Form Games (IIEFGs) (Kuhn, 1953). IIEFGs is a general formulation for multi-player games with both imperfect information (such as private information) and sequential play, and has been used for modeling and solving real-world games such as Poker (Heinrich et al, 2015;Moravčík et al, 2017;Sandholm, 2018, 2019), Bridge (Tian et al, 2020), Scotland Yard (Schmid et al, 2021), and so on. In a two-player zero-sum IIEFG, the standard solution concept is the celebrated notion of Nash Equilibrium (NE) (Nash et al, 1950), that is, a pair of independent policies for both players such that no player can gain by deviating from her own policy.…”

Section: Introductionmentioning

confidence: 99%

Sample-Efficient Learning of Correlated Equilibria in Extensive-Form Games

Song¹,

Song²

2022

Preprint

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Imperfect-Information Extensive-Form Games (IIEFGs) is a prevalent model for real-world games involving imperfect information and sequential plays. The Extensive-Form Correlated Equilibrium (EFCE) has been proposed as a natural solution concept for multi-player general-sum IIEFGs. However, existing algorithms for finding an EFCE require full feedback from the game, and it remains open how to efficiently learn the EFCE in the more challenging bandit feedback setting where the game can only be learned by observations from repeated playing.This paper presents the first sample-efficient algorithm for learning the EFCE from bandit feedback. We begin by proposing K-EFCE-a more generalized definition that allows players to observe and deviate from the recommended actions for K times. The K-EFCE includes the EFCE as a special case at K = 1, and is an increasingly stricter notion of equilibrium as K increases. We then design an uncoupled noregret algorithm that finds an ε-approximate K-EFCE within O(maxi XiA K i /ε 2 ) iterations in the full feedback setting, where Xi and Ai are the number of information sets and actions for the i-th player. Our algorithm works by minimizing a wide-range regret at each information set that takes into account all possible recommendation histories. Finally, we design a sample-based variant of our algorithm that learns an ε-approximate K-EFCE within O(maxi XiA K+1 i /ε 2 ) episodes of play in the bandit feedback setting. When specialized to K = 1, this gives the first sample-efficient algorithm for learning EFCE from bandit feedback.

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Player of Games

Cited by 13 publications

References 29 publications

The Accidental Philosopher and One of the Hardest Problems in the World

The Accidental Philosopher and One of the Hardest Problems in the World

Fast Algorithms for Poker Require Modelling it as a Sequential Bayesian Game

Sample-Efficient Learning of Correlated Equilibria in Extensive-Form Games

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