Related papers: Schrodinger Bridge over Averaged Systems
We consider a class of optimal control problems, with finite or infinite horizon, for a continuous-time Markov chain with finite state space. In this case, the control process affects the transition rates. We suppose that the controlled…
The Schrodinger Bridge and Bass (SBB) formulation, which jointly controls drift and volatility, is an established extension of the classical Schrodinger Bridge (SB). Building on this framework, we introduce LightSBB-M, an algorithm that…
We consider network routing under random link failures with a desired final distribution. We provide a mathematical formulation of a relaxed transport problem where the final distribution only needs to be close to the desired one. The…
Entropy-regularized optimal transport, which has strong links to the Schr\"odinger bridge problem in statistical mechanics, enjoys a variety of applications from trajectory inference to generative modeling. A major driver of renewed…
We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of…
The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…
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 study feedback control of coupled nonlinear stochastic oscillators in a force field. We first consider the problem of asymptotically driving the system to a desired {\em steady state} corresponding to reduced thermal noise. Among the…
Generative modeling typically seeks the path of least action via deterministic flows (ODE). While effective for in-distribution tasks, we argue that these deterministic paths become brittle under causal interventions, which often require…
Schr\"odinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based Generative Model (SGM). However,…
Denoising diffusion models are a novel class of generative models that have recently become extremely popular in machine learning. In this paper, we describe how such ideas can also be used to sample from posterior distributions and, more…
This paper considers stochastic-constrained stochastic optimization where the stochastic constraint is to satisfy that the expectation of a random function is below a certain threshold. In particular, we study the setting where data samples…
Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher…
Resampling from a target measure whose density is unknown is a fundamental problem in mathematical statistics and machine learning. A setting that dominates the machine learning literature consists of learning a map from an easy-to-sample…
We study an optimal control problem for a simple transportation model on a path graph. We give a closed form solution for the optimal controller, which can also account for planned disturbances using feed-forward. The optimal controller is…
We present an overview of our recent work on implementable solutions to the Schroedinger bridge problem and their potential application to optimal transport and various generalizations.
In this paper, we consider a chain of distributed systems governed by a degenerate parabolic equation, which satisfies a weak H\"{o}rmander type condition, with a control distributed over an open subdomain. In particular, we consider two…
We study single commodity network flows with suitable robustness and efficiency specs. An original use of a maximum entropy problem for distributions on the paths of the graph turns this problem into a steering problem for Markov chains…
We consider the problem of minimizing the entropy of a law with respect to the law of a reference branching Brownian motion under density constraints at an initial and final time. We call this problem the branching Schr\"odinger problem by…
Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the…