DOC IN PROGRESS

CLAUDIO MEGGIO: After briefly introducing the field of Reinforcement Learning and its mathematical formalism, I will explain Q-learning, one of the most famous model-free algorithms as well as its "deep" version developed at Deep Mind I will then present a case study which shows why the Reinforcement Learning problem is drastically harder in the multi-agent case compared to the classical single agent case, even when the multi-agent system is a simple zero-sum game with only 2 agents. In particular, I will explain how I applied some variants of Q-learning algorithms to the game of Connect 4 showing, as one might expect, that Independent Q-learning leads to instability, while minimax-Q converges to the optimal minimax strategy. MARGHERITA PAGANO: Un esempio di ostruzione di Brauer-Manin all’approssimazione debole proveniente da un primo con riduzione buona. Seguendo un articolo di Bright e Newton, costruiremo una superficie K3 sui numeri razionali avente riduzione buona nel primo 2, e per la quale 2 è l’unico primo avente buona riduzione coinvolto nell’ostruzione debole sulla superficie.