Related papers: Control, Transport and Sampling: Towards Better Lo…
In this paper, we study the Schr\"odinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin--endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure…
This paper addresses sampling-based trajectory optimization for risk-aware navigation under stochastic dynamics. Typically such approaches operate by computing $\tilde{N}$ perturbed rollouts around the nominal dynamics to estimate the…
Given two boundary distributions, the Schr\"odinger Bridge (SB) problem seeks the ``most likely`` random evolution between them with respect to a reference process. It has revealed rich connections to recent machine learning methods for…
Generative Semantic Communication (GSC) is a promising solution for image transmission over narrow-band and high-noise channels. However, existing GSC methods rely on long, indirect transport trajectories from a Gaussian to an image…
Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…
Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control…
In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…
Diffusion Schr\"odinger bridges (DSB) have recently emerged as a powerful framework for recovering stochastic dynamics via their marginal observations at different time points. Despite numerous successful applications, existing algorithms…
The aim of this paper is to recover displacement interpolations of probability measures, in the sense of the Optimal Transport theory, by semiclassical measures associated with solutions of Schr\"odinger equations defined on the flat torus.…
The unbalanced Schr\"odinger bridge problem (uSBP) seeks to interpolate between a probability measure $\rho_0$ and a sub-probability measure $\rho_T$ while minimizing KL divergence to a reference measure $\mathbf{R}$ on a path space. In…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
Visual navigation is a core challenge in Embodied AI, requiring autonomous agents to translate high-dimensional sensory observations into continuous, long-horizon action trajectories. While generative policies based on diffusion models and…
The static optimal transport $(\mathrm{OT})$ problem between Gaussians seeks to recover an optimal map, or more generally a coupling, to morph a Gaussian into another. It has been well studied and applied to a wide variety of tasks. Here we…
We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…
Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo…
Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of…
We characterize the Schr\"odinger bridge problems by a family of Mckean-Vlasov stochastic control problems with no terminal time distribution constraint. In doing so, we use the theory of Hilbert space embeddings of probability measures and…
Conditional generative models represent a significant advancement in the field of machine learning, allowing for the controlled synthesis of data by incorporating additional information into the generation process. In this work we introduce…
In this paper we show an effective means of integrating data driven frameworks to sampling based optimal control to vastly reduce the compute time for easy adoption and adaptation to real time applications such as on-road autonomous driving…
The Schr\"odinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized…