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Convergence of Monte Carlo Tree Search in Simultaneous Move Games
In this paper, we study Monte Carlo tree search (MCTS) in zero-sum extensive-form games with perfect information and simultaneous moves. We present a general template of MCTS algorithms for these games, which can be instantiated by various selection methods. We formally prove that if a selection method is $\epsilon$-Hannan consistent in a matrix game and satisfies additional requirements on exploration, then the MCTS algorithm eventually converges to an approximate Nash equilibrium (NE) of the extensive-form game. We empirically evaluate this claim using regret matching and Exp3 as the selection methods on randomly generated and worst case games. We confirm the formal result and show that additional MCTS variants also converge to approximate NE on the evaluated games.
Estimation in high-dimensional linear regression: Post-Double-Autometrics as an alternative to Post-Double-Lasso
Hué, Sullivan, Laurent, Sébastien, Aiounou, Ulrich, Flachaire, Emmanuel
Post-Double-Lasso is becoming the most popular method for estimating linear regression models with many covariates when the purpose is to obtain an accurate estimate of a parameter of interest, such as an average treatment effect. However, this method can suffer from substantial omitted variable bias in finite sample. We propose a new method called Post-Double-Autometrics, which is based on Autometrics, and show that this method outperforms Post-Double-Lasso.
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