Related papers: Generalized replicator dynamics based on mean-fiel…

Trial-and-error based reinforcement learning (RL) has seen rapid advancements in recent times, especially with the advent of deep neural networks. However, the majority of autonomous RL algorithms require a large number of interactions with…

We study the problem of detecting and localizing multiple changes in the mean parameter of a Banach space-valued time series. The goal is to construct a collection of narrow confidence intervals, each containing at least one (or exactly…

Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential…

Multi-scene reinforcement learning involves training the RL agent across multiple scenes / levels from the same task, and has become essential for many generalization applications. However, the inclusion of multiple scenes leads to an…

We study the dynamics of a family of replicator maps, depending on two parameters. Such studies are motivated by the analysis of the dynamics of evolutionary games under selections. From the dynamics viewpoint, we prove the existence of…

Reinforcement learning (RL) typically models the interaction between the agent and environment as a Markov decision process (MDP), where the rewards that guide the agent's behavior are always observable. However, in many real-world…

Generative adversarial network (GAN) is among the most popular deep learning models for learning complex data distributions. However, training a GAN is known to be a challenging task. This is often attributed to the lack of correlation…

The replicator equation is interpreted as a continuous inference equation and a formal similarity between the discrete replicator equation and Bayesian inference is described. Further connections between inference and the replicator…

We study a general class of fully coupled backward-forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the…

We consider three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise proportional imitation, and the exponential / multiplicative…

We study the generalized conditional gradient (GCG) method for time-dependent second-order mean field games (MFG) with local coupling terms. While explicit convergence rates of the GCG method were previously established only for globally…

Mean field games (MFG) and mean field control problems (MFC) are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative games with a…

This paper provides a unifying view of a wide range of problems of interest in machine learning by framing them as the minimization of functionals defined on the space of probability measures. In particular, we show that generative…

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…

The linear Markov Decision Process (MDP) framework offers a principled foundation for reinforcement learning (RL) with strong theoretical guarantees and sample efficiency. However, its restrictive assumption-that both transition dynamics…

We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths…

When a spatial process is recorded over time and the observation at a given time instant is viewed as a point in a function space, the result is a time series taking values in a Banach space. To study the spatio-temporal extremal dynamics…

The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…

A Coefficient Inverse Problem (CIP) of the determination of a coefficient of the Mean Field Games System (MFGS) of the second order is considered. The input data are generated by a single measurement event. Lateral Cauchy data, i.e.…

In multi-agent dynamic games, the Nash equilibrium state trajectory of each agent is determined by its cost function and the information pattern of the game. However, the cost and trajectory of each agent may be unavailable to the other…