Fast Convergence of Regularized Learning in GamesFast Convergence of Regularized Learning in GamesSyrgkanis, Vasilis and Agarwal, Alekh and Luo, Haipeng and Schapire, Robert E.2015

Paper summarynipsreviewsThe authors perform theoretical analysis about faster convergence with multi-player normal-form games by generalizing techniques for two-player zero-sum games. They also perform empirical evaluation by using the 4-bidder simultaneous auction game.
The paper is concerned with two problems:
1. How does the social welfare of players using regret minimization algorithms compare to the optimal welfare.
2. Can one obtain better regret bounds when all players use a regret minimization algorithm
The paper deals with bounds on regret minimization algorithms in games. The usual regret bounds on these algorithms is in $O(\sqrt{T})$. However, this assumes that the learner faces a completely adversarial opponent. However, it is natural to assume that on a game everyone will play a regret minimization algorithm and the question is whether or not one can obtain better rates in this scenario. The authors show that regret in $O(T^{1/4})$ is achievable for general games.

The authors perform theoretical analysis about faster convergence with multi-player normal-form games by generalizing techniques for two-player zero-sum games. They also perform empirical evaluation by using the 4-bidder simultaneous auction game.
The paper is concerned with two problems:
1. How does the social welfare of players using regret minimization algorithms compare to the optimal welfare.
2. Can one obtain better regret bounds when all players use a regret minimization algorithm
The paper deals with bounds on regret minimization algorithms in games. The usual regret bounds on these algorithms is in $O(\sqrt{T})$. However, this assumes that the learner faces a completely adversarial opponent. However, it is natural to assume that on a game everyone will play a regret minimization algorithm and the question is whether or not one can obtain better rates in this scenario. The authors show that regret in $O(T^{1/4})$ is achievable for general games.

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