Related papers: Random Features for High-Dimensional Nonlocal Mean…

In this work, we consider a novel inverse problem in mean-field games (MFG). We aim to recover the MFG model parameters that govern the underlying interactions among the population based on a limited set of noisy partial observations of the…

We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in Bayraktar, Budhiraja, and Cohen (2017). The MFG is formulated in terms of a…

Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…

Mean field games (MFGs) are a promising framework for modeling the behavior of large-population systems. However, solving MFGs can be challenging due to the coupling of forward population evolution and backward agent dynamics. Typically,…

Learning the behavior of large agent populations is an important task for numerous research areas. Although the field of multi-agent reinforcement learning (MARL) has made significant progress towards solving these systems, solutions for…

We establish the convergence of the deep actor-critic reinforcement learning algorithm presented in [Angiuli et al., 2023a] in the setting of continuous state and action spaces with an infinite discrete-time horizon. This algorithm provides…

This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis…

Kernel learning methods are among the most effective learning methods and have been vigorously studied in the past decades. However, when tackling with complicated tasks, classical kernel methods are not flexible or "rich" enough to…

We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM…

In this paper, we use mean field games (MFGs) to investigate approximations of $N$-player games with uniformly symmetrically continuous heterogeneous closed-loop actions. To incorporate agents' risk aversion (beyond the classical expected…

We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…

Mean field games (MFGs) describe the collective behavior of large populations of interacting agents. In this work, we tackle ill-posed inverse problems in potential MFGs, aiming to recover the agents' population, momentum, and environmental…

This paper proposes using a linear function approximator, rather than a deep neural network (DNN), to bias a Monte Carlo tree search (MCTS) player for general games. This is unlikely to match the potential raw playing strength of DNNs, but…

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

Learning in multi-agent systems is highly challenging due to several factors including the non-stationarity introduced by agents' interactions and the combinatorial nature of their state and action spaces. In particular, we consider the…

Markov Random Fields (MRFs), a formulation widely used in generative image modeling, have long been plagued by the lack of expressive power. This issue is primarily due to the fact that conventional MRFs formulations tend to use simplistic…

Modern robotic systems frequently engage in complex multi-agent interactions, many of which are inherently multi-modal, i.e., they can lead to multiple distinct outcomes. To interact effectively, robots must recognize the possible…

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…

We propose a new class of random feature methods for linearizing softmax and Gaussian kernels called hybrid random features (HRFs) that automatically adapt the quality of kernel estimation to provide most accurate approximation in the…

We study infinite horizon discounted Mean Field Control (MFC) problems with common noise through the lens of Mean Field Markov Decision Processes (MFMDP). We allow the agents to use actions that are randomized not only at the individual…