Related papers: Multi-marginal Schrodinger bridges
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
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…
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox…
We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location with a generic space-dependent rate of resetting. We present a systematic approach…
We consider particles that are conditioned to initial and final states. The trajectory of these particles is uniquely shaped by the intricate interplay of internal and external sources of randomness. The internal randomness is aptly…
The Schr\"odinger Bridge (SB) problem has become a fundamental tool in computational optimal transport and generative modeling. To address this problem, ideal methods such as Iterative Proportional Fitting and Iterative Markovian Fitting…
We establish the stability of solutions to the entropically regularized optimal transport problem with respect to the marginals and the cost function. The result is based on the geometric notion of cyclical invariance and inspired by the…
We investigate the statistical properties of an over-damped Brownian particle that is trapped by a harmonic potential and simultaneously exposed to a linear shear flow or to a plane Poiseuille flow. Its probability distribution is…
Homotopy approaches to Bayesian inference have found widespread use especially if the Kullback-Leibler divergence between the prior and the posterior distribution is large. Here we extend one of these homotopy approach to include an…
We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…
The computation of the probability of the first-passage time through a given threshold of a stochastic process is a classic problem that appears in many branches of physics. When the stochastic dynamics is markovian, the probability admits…
The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the…
Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid…
We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. In this paper, we build on previous work combining Schr\"odinger bridges and plug & play Langevin…
We present a theoretical framework that reinterprets Population Annealing (PA) through the lens of the discrete-time Schr\"odinger Bridge (SB) problem. We demonstrate that the heuristic reweighting step in PA is derived by analytically…
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)…
We establish the uniform in time stability, w.r.t. the marginals, of the Iterative Proportional Fitting Procedure, also known as Sinkhorn algorithm, used to solve entropy-regularised Optimal Transport problems. Our result is quantitative…
We study existence of probability measure valued jump-diffusions described by martingale problems. We develop a simple device that allows us to embed Wasserstein spaces and other similar spaces of probability measures into locally compact…
Efficient particle sorting in microfluidic systems is vital for advancements in biomedical diagnostics and industrial applications. This study numerically investigates particle migration and passive sorting in symmetric serpentine…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…