Related papers: Generative Modeling by Value-Driven Transport
This paper investigates the problem of regulating in real time a linear dynamical system to the solution trajectory of a time-varying constrained convex optimization problem. The proposed feedback controller is based on an adaptation of the…
We connect a broad class of generative models through their shared reliance on sequential decision making. Motivated by this view, we develop extensions to an existing model, and then explore the idea further in the context of data…
Generative models, particularly diffusion models, have achieved remarkable success in density estimation for multimodal data, drawing significant interest from the reinforcement learning (RL) community, especially in policy modeling in…
Generative design refers to computational design methods that can automatically conduct design exploration under constraints defined by designers. Among many approaches, topology optimization-based generative designs aim to explore diverse…
This work considers the sample and computational complexity of obtaining an $\epsilon$-optimal policy in a discounted Markov Decision Process (MDP), given only access to a generative model. In this work, we study the effectiveness of the…
Direct simulation of the von Neumann dynamics for a general (pure or mixed) quantum state can often be expensive. One prominent example is the real-time time-dependent density functional theory (rt-TDDFT), a widely used framework for the…
Whilst optimal transport (OT) is increasingly being recognized as a powerful and flexible approach for dealing with fairness issues, current OT fairness methods are confined to the use of discrete OT. In this paper, we leverage recent…
Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…
Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
Learning-based approaches are increasingly popular for traffic control problems. However, these approaches are applied typically as black boxes with limited theoretical guarantees and interpretability. In this paper, we consider the theory…
Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
We propose a new stochastic primal-dual optimization algorithm for planning in a large discounted Markov decision process with a generative model and linear function approximation. Assuming that the feature map approximately satisfies…
In the domain of autonomous vehicles (AVs), decision-making is a critical factor that significantly influences the efficacy of autonomous navigation. As the field progresses, the enhancement of decision-making capabilities in complex…
We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution $P_X$ and the latent variable model distribution $P_G$. We show that the OT problem can be equivalently…
Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled…
The theory of Optimal Transport (OT) and Martingale Optimal Transport (MOT) were inspired by problems in economics and finance and have flourished over the past decades, making significant advances in theory and practice. MOT considers the…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…