English
Related papers

Related papers: Schrodinger Bridge over Averaged Systems

200 papers

We consider the problem of steering an initial probability density for the state vector of a linear system to a final one, in finite time, using minimum energy control. In the case where the dynamics correspond to an integrator ($\dot x(t)…

Optimization and Control · Mathematics 2015-02-05 Yongxin Chen , Tryphon Georgiou , Michele Pavon

Schrodinger Bridges (SBs) are diffusion processes that steer, in finite time, a given initial distribution to another final one while minimizing a suitable cost functional. Although various methods for computing SBs have recently been…

Machine Learning · Computer Science 2025-10-15 George Rapakoulias , Ali Reza Pedram , Fengjiao Liu , Lingjiong Zhu , Panagiotis Tsiotras

This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal…

Probability · Mathematics 2026-03-31 Camilo Hernández , Ludovic Tangpi

The Mean-Field Schrodinger Bridge (MFSB) problem is an optimization problem aiming to find the minimum effort control policy to drive a McKean-Vlassov stochastic differential equation from one probability measure to another. In the context…

Machine Learning · Computer Science 2025-06-19 George Rapakoulias , Ali Reza Pedram , Panagiotis Tsiotras

We consider the problem of steering a linear stochastic system between two end-point degenerate Gaussian distributions in finite time. This accounts for those situations in which some but not all of the state entries are uncertain at the…

Optimization and Control · Mathematics 2020-06-18 Valentina Ciccone , Yongxin Chen , Tryphon T. Georgiou , Michele Pavon

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…

Machine Learning · Computer Science 2023-11-02 Nikita Gushchin , Alexander Kolesov , Alexander Korotin , Dmitry Vetrov , Evgeny Burnaev

The Schr\"odinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates…

Machine Learning · Computer Science 2024-11-06 Nikita Gushchin , Daniil Selikhanovych , Sergei Kholkin , Evgeny Burnaev , Alexander Korotin

We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics. Since the direct Schr\"odinger bridge between Gaussian mixtures is generally not available in closed form, we introduce a…

Optimization and Control · Mathematics 2026-05-26 Siddhartha Ganguly , George Rapakoulias , Panagiotis Tsiotras

Score-based generative models have recently attracted significant attention for their ability to generate high-fidelity data by learning maps from simple Gaussian priors to complex data distributions. A natural generalization of this idea…

Computation · Statistics 2025-11-19 Hanwen Huang

Modern distribution matching algorithms for training diffusion or flow models directly prescribe the time evolution of the marginal distributions between two boundary distributions. In this work, we consider a generalized distribution…

We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…

Systems and Control · Computer Science 2014-07-15 Yongxin Chen , Tryphon Georgiou

Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schr\"odinger bridge matching, effectively learn mappings…

Machine Learning · Computer Science 2026-03-03 Sophia Tang , Yinuo Zhang , Alexander Tong , Pranam Chatterjee

Modern methods of generative modelling and unpaired data translation based on Schr\"odinger bridges and stochastic optimal control theory aim to transform an initial density to a target one in an optimal way. In the present paper, we assume…

Machine Learning · Computer Science 2026-03-24 Nikita Puchkin , Denis Suchkov , Alexey Naumov , Denis Belomestny

In this article, we present a general methodology for control problems driven by the Brownian motion filtration including non-Markovian and non-semimartingale state processes controlled by mutually singular measures. The main result of this…

Probability · Mathematics 2018-01-19 Dorival Leão , Alberto Ohashi , Francys Souza

This work studies the Schr\"odinger bridge problem for the kinematic equation on a compact connected Lie group. The objective is to steer a controlled diffusion between given initial and terminal densities supported over the Lie group while…

Optimization and Control · Mathematics 2026-03-23 Hamza Mahmood , Abhishek Halder , Adeel Akhtar

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…

We consider the problem to identify the most likely flow in phase space, of (inertial) particles under stochastic forcing, that is in agreement with spatial (marginal) distributions that are specified at a set of points in time. The…

Optimization and Control · Mathematics 2019-02-25 Yongxin Chen , Giovanni Conforti , Tryphon T. Georgiou , Luigia Ripani

Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…

Statistics Theory · Mathematics 2024-05-28 Sören Christensen , Claudia Strauch , Lukas Trottner

The Schr\"{o}dinger Bridge Problem (SBP), which can be understood as an entropy-regularized optimal transport, seeks to compute stochastic dynamic mappings connecting two given distributions. SBP has shown significant theoretical importance…

Optimization and Control · Mathematics 2025-03-25 Yang Jing , Lei Li , Jingtong Zhang

In this paper, we establish a general stochastic maximum principle for optimal control for systems described by a continuous-time Markov regime-switching stochastic recursive utilities model. The control domain is postulated not to be…

Optimization and Control · Mathematics 2019-05-02 Liangquan Zhang , Xun Li