Related papers: A Conversation with James Hannan
H\"older stability estimate and uniqueness are proven for a retrospective problem of Mean Field Games with a non-quadratic Hamiltonian. The previous result was only for the quadratic Hamiltonian. The main tool is the apparatus of Carleman…
This is an expanded version of the lecture given at the AMS Short Course on Mean Field Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of Mean Field Games in finance and economics. I need to admit upfront…
We study biased {\em orientation games}, in which the board is the complete graph $K_n$, and Maker and Breaker take turns in directing previously undirected edges of $K_n$. At the end of the game, the obtained graph is a tournament. Maker…
We applied a variety of parametric and non-parametric machine learning models to predict the probability distribution of rainfall based on 1M training examples over a single year across several U.S. states. Our top performing model based on…
We consider the problem of predicting human players' actions in repeated strategic interactions. Our goal is to predict the dynamic step-by-step behavior of individual players in previously unseen games. We study the ability of neural…
We introduce a new type of Mean Field Game epidemiological models, in which subpopulations have different behavioral patterns: some are viewed as "highly rational" (choosing Nash-equilibrium long-term strategies) while others follow…
Volatility is a natural risk measure in finance as it quantifies the variation of stock prices. A frequently considered problem in mathematical finance is to forecast different estimates of volatility. What makes it promising to use deep…
Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis. Optimal strategies may require randomisation when dealing with inherently…
It is a long-standing goal of artificial intelligence (AI) to be superior to human beings in decision making. Games are suitable for testing AI capabilities of making good decisions in non-numerical tasks. In this paper, we develop a new AI…
It is well known that artificial neural networks (ANNs) can learn deterministic automata. Learning nondeterministic automata is another matter. This is important because much of the world is nondeterministic, taking the form of…
We introduce a "high probability" framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high…
Planning is essential for solving complex tasks, yet the internal mechanisms underlying planning in neural networks remain poorly understood. Building on prior work, we analyze a recurrent neural network (RNN) trained on Sokoban, a…
This report first provides a brief overview of a number of supervised learning algorithms for regression tasks. Among those are neural networks, regression trees, and the recently introduced Nexting. Nexting has been presented in the…
We consider how an agent should update her uncertainty when it is represented by a set P of probability distributions and the agent observes that a random variable X takes on value x, given that the agent makes decisions using the minimax…
Poker is a multiplayer game of imperfect information and has been widely studied in game theory. Many popular variants of poker (e.g., Texas Hold'em and Omaha) at the edge of modern game theory research are large games. However, even toy…
Fictitious play is a simple and widely studied adaptive heuristic for playing repeated games. It is well known that fictitious play fails to be Hannan consistent. Several variants of fictitious play including regret matching, generalized…
On average once every four years, the Tropical Pacific warms considerably during events called El Ni\~no, leading to weather disruptions over many regions on Earth. Recent machine-learning approaches to El Ni\~no prediction, in particular…
A contrarian is someone who deliberately decides to oppoe the prevailing choice of others. The Galam model of two state opinion dynamicsincorporates agent updates by a single step random grouping in which all participants adopt the opinion…
The success of deep learning techniques over the last decades has opened up a new avenue of research for weather forecasting. Here, we take the novel approach of using a neural network to predict full probability density functions at each…
We propose a didactic approach to use the Machine Learning protocol in order to perform weather forecast. This study is motivated by the possibility to apply this method to predict weather conditions in proximity of the Etna and Stromboli…