In this work, we introduce a new Markov operator associated with a digraph, which we refer to as a nonlinear Laplacian. Unlike previous Laplacians for digraphs, the nonlinear Laplacian does not rely on the stationary distribution of the random walk process and is well defined on digraphs that are not strongly connected. We show that the nonlinear Laplacian has nontrivial eigenvalues and give a Cheeger-like inequality, which relates the conductance of a digraph and the smallest non-zero eigenvalue of its nonlinear Laplacian. Finally, we apply the nonlinear Laplacian to the analysis of real-world networks and obtain encouraging results.
- The document introduces Deep Counterfactual Regret Minimization (Deep CFR), a new algorithm proposed by Noam Brown et al. in ICML 2019 that incorporates deep neural networks into Counterfactual Regret Minimization (CFR) for solving large imperfect-information games.
- CFR is an algorithm for computing Nash equilibria in two-player zero-sum games by minimizing cumulative counterfactual regret. It scales poorly to very large games that require abstraction of the game tree.
- Deep CFR removes the need for abstraction by using a neural network to generalize the strategy across the game tree, allowing it to solve previously intractable games like no-limit poker.
NagoyaStat #12 で使用した資料です(公開に当たって当日ホワイトボードに書いた内容等を補完したものになります)。
「StanとRでベイズ統計モデリング」の第9章前半になります。
第9章のテーマは行列やベクトルを使った演算の高速化です。
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The title of textbook is "Bayesian statistical modeling with Stan and R", and that of Chapter 9 in textbook is "advanced grammar" in English.
- The document introduces Deep Counterfactual Regret Minimization (Deep CFR), a new algorithm proposed by Noam Brown et al. in ICML 2019 that incorporates deep neural networks into Counterfactual Regret Minimization (CFR) for solving large imperfect-information games.
- CFR is an algorithm for computing Nash equilibria in two-player zero-sum games by minimizing cumulative counterfactual regret. It scales poorly to very large games that require abstraction of the game tree.
- Deep CFR removes the need for abstraction by using a neural network to generalize the strategy across the game tree, allowing it to solve previously intractable games like no-limit poker.
NagoyaStat #12 で使用した資料です(公開に当たって当日ホワイトボードに書いた内容等を補完したものになります)。
「StanとRでベイズ統計モデリング」の第9章前半になります。
第9章のテーマは行列やベクトルを使った演算の高速化です。
---
The title of textbook is "Bayesian statistical modeling with Stan and R", and that of Chapter 9 in textbook is "advanced grammar" in English.