Conditional Versus Adversarial Euler-based Generators For Time Series

We introduce new generative models for time series based on Euler discretization that do not require any pre-stationarization procedure. Specifically, we develop two GAN based methods, relying on the adaptation of Wasserstein GANs (Arjovsky et al., 2017) and DVD GANs (Clark et al., 2019b) to time series. Alternatively, we consider a conditional Euler Generator (CEGEN) minimizing a distance between the induced conditional densities. In the context of It\^o processes, we theoretically validate this approach and demonstrate using the Bures metric that reaching a low loss level provides accurate estimations for both the drift and the volatility terms of the underlying process. Tests on simple models show how the Euler discretization and the use of Wasserstein distance allow the proposed GANs and (more considerably) CEGEN to outperform state-of-the-art Time Series GAN generation( Yoon et al., 2019b) on time structure metrics. In higher dimensions we observe that CEGEN manages to get the correct covariance structures. Finally we illustrate how our model can be combined to a Monte Carlo simulator in a low data context by using a transfer learning technique

Game Plan: What AI can do for Football, and What Football can do for AI

The rapid progress in artificial intelligence (AI) and machine learning has opened unprecedented analytics possibilities in various team and individual sports, including baseball, basketball, and tennis. More recently, AI techniques have been applied to football, due to a huge increase in data collection by professional teams, increased computational power, and advances in machine learning, with the goal of better addressing new scientific challenges involved in the analysis of both individual players' and coordinated teams' behaviors. The research challenges associated with predictive and prescriptive football analytics require new developments and progress at the intersection of statistical learning, game theory, and computer vision. In this paper, we provide an overarching perspective highlighting how the combination of these fields, in particular, forms a unique microcosm for AI research, while offering mutual benefits for professional teams, spectators, and broadcasters in the years to come. We illustrate that this duality makes football analytics a game changer of tremendous value, in terms of not only changing the game of football itself, but also in terms of what this domain can mean for the field of AI. We review the state-of-the-art and exemplify the types of analysis enabled by combining the aforementioned fields, including illustrative examples of counterfactual analysis using predictive models, and the combination of game-theoretic analysis of penalty kicks with statistical learning of player attributes. We conclude by highlighting envisioned downstream impacts, including possibilities for extensions to other sports (real and virtual).

Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications

In this paper, we deepen the analysis of continuous time Fictitious Play learning algorithm to the consideration of various finite state Mean Field Game settings (finite horizon, $\gamma$-discounted), allowing in particular for the introduction of an additional common noise. We first present a theoretical convergence analysis of the continuous time Fictitious Play process and prove that the induced exploitability decreases at a rate $O(\frac{1}{t})$. Such analysis emphasizes the use of exploitability as a relevant metric for evaluating the convergence towards a Nash equilibrium in the context of Mean Field Games. These theoretical contributions are supported by numerical experiments provided in either model-based or model-free settings. We provide hereby for the first time converging learning dynamics for Mean Field Games in the presence of common noise.

Reinforcement Learning in Economics and Finance

Reinforcement learning algorithms describe how an agent can learn an optimal action policy in a sequential decision process, through repeated experience. In a given environment, the agent policy provides him some running and terminal rewards. As in online learning, the agent learns sequentially. As in multi-armed bandit problems, when an agent picks an action, he can not infer ex-post the rewards induced by other action choices. In reinforcement learning, his actions have consequences: they influence not only rewards, but also future states of the world. The goal of reinforcement learning is to find an optimal policy -- a mapping from the states of the world to the set of actions, in order to maximize cumulative reward, which is a long term strategy. Exploring might be sub-optimal on a short-term horizon but could lead to optimal long-term ones. Many problems of optimal control, popular in economics for more than forty years, can be expressed in the reinforcement learning framework, and recent advances in computational science, provided in particular by deep learning algorithms, can be used by economists in order to solve complex behavioral problems. In this article, we propose a state-of-the-art of reinforcement learning techniques, and present applications in economics, game theory, operation research and finance.

Approximate Fictitious Play for Mean Field Games

The theory of Mean Field Games (MFG) allows characterizing the Nash equilibria of an infinite number of identical players, and provides a convenient and relevant mathematical framework for the study of games with a large number of agents in interaction. Until very recently, the literature only considered Nash equilibria between fully informed players. In this paper, we focus on the realistic setting where agents with no prior information on the game learn their best response policy through repeated experience. We study the convergence to a (possibly approximate) Nash equilibrium of a fictitious play iterative learning scheme where the best response is approximately computed, typically by a reinforcement learning (RL) algorithm. Notably, we show for the first time convergence of model free learning algorithms towards non-stationary MFG equilibria, relying only on classical assumptions on the MFG dynamics. We illustrate our theoretical results with a numerical experiment in continuous action-space setting, where the best response of the iterative fictitious play scheme is computed with a deep RL algorithm.