Learning Sparse Polymatrix Games in Polynomial Time and Sample Complexity
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Proceedings of the TwentyFirst International Conference on Artificial Intelligence and Statistics, PMLR 84:14861494, 2018.
Abstract
We consider the problem of learning sparse polymatrix games from observations of strategic interactions. We show that a polynomial time method based on $\ell_{1,2}$group regularized logistic regression recovers a game, whose Nash equilibria are the $ε$Nash equilibria of the game from which the data was generated (true game), in $O(m^4 d^4 \log (pd))$ samples of strategy profiles — where $m$ is the maximum number of pure strategies of a player, $p$ is the number of players, and $d$ is the maximum degree of the game graph. Under slightly more stringent separability conditions on the payoff matrices of the true game, we show that our method learns a game with the exact same Nash equilibria as the true game. We also show that $Ω(d \log (pm))$ samples are necessary for any method to consistently recover a game, with the same Nashequilibria as the true game, from observations of strategic interactions.
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