Related papers: Deep Generalized Schr\"odinger Bridge
Recent advancements in diffusion bridges for distribution transport problems have heavily relied on matching frameworks, yet existing methods often face a trade-off between scalability and access to optimal pairings during training. Fully…
We study Diffusion Schr\"odinger Bridge (DSB) models in the context of dynamical astrophysical systems, specifically tackling observational inverse prediction tasks within Giant Molecular Clouds (GMCs) for star formation. We introduce the…
Mean Field Games (MFGs) provide a principled framework for modelling interactions in large population systems. However, algorithmic progress has been limited since model-free methods are high variance and exact methods scale poorly. Recent…
The dynamic Schr\"odinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as optimal transport problems. It consists of learning non-linear diffusion processes using efficient…
Deep Ensemble (DE) approach is a straightforward technique used to enhance the performance of deep neural networks by training them from different initial points, converging towards various local optima. However, a limitation of this…
In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a Mean Field Game (MFG). This is a noticeable change since usually mathematical frameworks focus on one large trader in front of a…
In a regular mean field game (MFG), the agents are assumed to be insignificant, they do not realize their effect on the population level and this may result in a phenomenon coined as the Tragedy of the Commons by the economists. However, in…
Modern machine learning models are typically trained via multi-pass stochastic gradient descent (SGD) with small batch sizes, and understanding their dynamics in high dimensions is of great interest. However, an analytical framework for…
Diffusion models serve as a powerful generative framework for solving inverse problems. However, they still face two key challenges: 1) the distortion-perception tradeoff, where improving perceptual quality often degrades reconstruction…
The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative…
We propose a policy iteration method to solve an inverse problem for a mean-field game (MFG) model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the…
Mean Field Games (MFGs) provide a powerful framework for modeling the collective behavior of large populations of interacting agents. In this paper, we address the problem of Imitation Learning (IL) in MFGs subject to common noise, where…
We consider anonymous multi-agent path finding (MAPF) where a set of robots is tasked to travel to a set of targets on a finite, connected graph. We show that MAPF can be cast as a special class of multi-marginal optimal transport (MMOT)…
Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…
In this work, we study the mean field Schr\"odinger problem from a purely probabilistic point of view by exploiting its connection to stochastic control theory for McKean-Vlasov diffusions. Our main result shows that the mean field…
This paper investigates the control of a massive population of UAVs such as drones. The straightforward method of control of UAVs by considering the interactions among them to make a flock requires a huge inter-UAV communication which is…
We study mean-field game (MFG) problems with rough common noise, in which the representative state dynamics are governed by a controlled rough stochastic differential equation driven by an idiosyncratic Brownian motion and a deterministic…
We propose to learn a generative model via entropy interpolation with a Schr\"{o}dinger Bridge. The generative learning task can be formulated as interpolating between a reference distribution and a target distribution based on the…
Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from…
Mean field type games (MFTGs) describe Nash equilibria between large coalitions: each coalition consists of a continuum of cooperative agents who maximize the average reward of their coalition while interacting non-cooperatively with a…