Deep Q-Learning for Nash Equilibria: Nash-DQN

Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games, and are applicable only in small state-action spaces or other simplified settings. Here, we develop a new data efficient Deep-Q-learning methodology for model-free learning of Nash equilibria for general-sum stochastic games. The algorithm uses a local linear-quadratic expansion of the stochastic game, which leads to analytically solvable optimal actions. The expansion is parametrized by deep neural networks to give it sufficient flexibility to learn the environment without the need to experience all state-action pairs. We study symmetry properties of the algorithm stemming from label-invariant stochastic games and as a proof of concept, apply our algorithm to learning optimal trading strategies in competitive electronic markets.Comment: 16 pages, 4 figure

Israeli Reactions

Josephine D. Casgrain comments and records an article published in the newspaper, Al Ha-mishmar, regarding Pope John XXIII\u27s revision of the Good Friday prayer

Israeli Reactions

Josephine D. Casgrain comments and records an article published in the newspaper, Al Ha-mishmar, regarding Pope John XXIII\u27s revision of the Good Friday prayer

Bolivie, Chili et Pérou : éternelles disputes, nouveaux enjeux

En janvier 2008, le Pérou a déposé un recours à la Cour internationale de Justice pour fixer sa frontière maritime avec le Chili. Symptômes des enjeux conjoncturels, les différends territoriaux du Nord chilien d’aujourd’hui sont intimement liés aux stratégies nationales pour contrôler le secteur énergétique, ainsi qu’à la compétition entre différents projets d’intégration régionale. En plus d’irriter Santiago, les revendications maritimes de Lima sont un affront à la Bolivie. Le renouveau de la Bolivie, inspiré par son président indigène et sa nouvelle Constitution, ne saurait réussir sans régler une fois pour toutes son accès maritime, perdu en 1884 à l’issu de la Guerre du Pacifique, et dont les Boliviens persistent à y voir une flagrante injustice envers leur nation. Au niveau régional, la stratégie revendicative de Lima s’inscrit dans une suite de tensions entre pays de diverses allégences idéologiques, et la crainte d’une course aux armements, dans le sous-continent sud-américain

Jurisdiction, Fairness and Reasonableness

There is no doubt that in the days of procedural refinements, arbitrary distinctions and uncertainty as to the purpose of judicial review, the subject was exceedingly complicated and unnecessarily subtle. With the new dominance of relatively simple concepts, and more obvious policy goals, we may reduce the subject to a wholesome simplicity, so that both the government and the citizens can know and understand their rights. To do so, we have to consider the fundamental concepts one by one, and then apply them to recent jurisprudence and to the policy of modern administrative law