36 citations · 122 across the 31 of their papers we have counts for
31 papers
Gradient Flows as Optimal Controlled Evolutions: From Rn to Wasserstein product spaces
Yongxin Chen, Tryphon Georgiou, Michele Pavon
We show that the continuous-time gradient descent in Rn can be viewed as an optimal controlled evolution for a suitable action functional; a similar result holds for stochastic gra…
Control and estimation of multi-commodity network flow under aggregation
Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
A paradigm put forth by E. Schrödinger in 1931/32, known as Schrödinger bridges, represents a formalism to pose and solve control and estimation problems seeking a perturbation fro…
The most likely evolution of diffusing and vanishing particles: Schrodinger Bridges with unbalanced marginals
Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
Stochastic flows of an advective-diffusive nature are ubiquitous in physical sciences. Of particular interest is the problem to reconcile observed marginal distributions with a giv…
Optimal steering to invariant distributions for networks flows
Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
We derive novel results on the ergodic theory of irreducible, aperiodic Markov chains. We show how to optimally steer the network flow to a stationary distribution over a finite or…
Stochastic control liaisons: Richard Sinkhorn meets Gaspard Monge on a Schroedinger bridge
Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
In 1931/32, Schroedinger studied a hot gas Gedankenexperiment, an instance of large deviations of the empirical distribution and an early example of the so-called maximum entropy i…
Covariance steering in zero-sum linear-quadratic two-player differential games
Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
We formulate a new class of two-person zero-sum differential games, in a stochastic setting, where a specification on a target terminal state distribution is imposed on the players…
Probabilistic Kernel Support Vector Machines
Yongxin Chen, Tryphon T. Georgiou, Allen R. Tannenbaum
We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a descri…
Optimal steering for non-Markovian Gaussian processes
Daniele Alpago, Yongxin Chen, Tryphon Georgiou +1
At present, the problem to steer a non-Markovian process with minimum energy between specified end-point marginal distributions remains unsolved. Herein, we consider the special ca…
Multi-marginal Schrodinger bridges
Yongxin Chen, Giovanni Conforti, Tryphon T. Georgiou +1
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) distribution…
Ruelle-Bowen continuous-time random walk
Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
We define the probability structure of a continuous-time time-homogeneous Markov jump process, on a finite graph, that represents the continuous-time counterpart of the so-called R…
Measure-valued spline curves: an optimal transport viewpoint
Yongxin Chen, Giovanni Conforti, Tryphon T. Georgiou
The aim of this article is to introduce and address the problem to smoothly interpolate (empirical) probability measures. To this end, we lift the concept of a spline curve from th…
Steering the distribution of agents in mean-field and cooperative games
Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
The purpose of this work is to pose and solve the problem to guide a collection of weakly interacting dynamical systems (agents, particles, etc.) to a specified terminal distributi…
Optimal transport for Gaussian mixture models
Yongxin Chen, Tryphon T. Georgiou, Allen Tannenbaum
We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare…
An Efficient Algorithm for Matrix-Valued and Vector-Valued Optimal Mass Transport
Yongxin Chen, Eldad Haber, Kaoru Yamamoto +2
We present an efficient algorithm for recent generalizations of optimal mass transport theory to matrix-valued and vector-valued densities. These generalizations lead to several ap…
Interpolation of Density Matrices and Matrix-Valued Measures: The Unbalanced Case
Yongxin Chen, Tryphon T. Georgiou, Allen Tannenbaum
In this note, we propose an unbalanced version of the quantum mechanical version of optimal mass transport that was based on the Lindblad equation. We formulate a natural interpola…
On the Matrix Monge-Kantorovich Problem
Yongxin Chen, Wilfrid Gangbo, Tryphon T. Georgiou +1
The classical Monge-Kantorovich (MK) problem as originally posed is concerned with how best to move a pile of soil or rubble to an excavation or fill with the least amount of work…
Vector-Valued Optimal Mass Transport
Yongxin Chen, Tryphon T. Georgiou, Allen Tannenbaum
We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete o…
Robust transport over networks
Yongxin Chen, Tryphon T. Georgiou, Michele Pavon +1
We consider transport over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed…
Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces
Yongxin Chen, Tryphon Georgiou, Michele Pavon
Since the early nineties, it has been observed that the Schroedinger bridge problem can be formulated as a stochastic control problem with atypical boundary constraints. This in tu…
Entropic and displacement interpolation: a computational approach using the Hilbert metric
Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
Monge-Kantorovich optimal mass transport (OMT) provides a blueprint for geometries in the space of positive densities -- it quantifies the cost of transporting a mass distribution…
Steering state statistics with output feedback
Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
Consider a linear stochastic system whose initial state is a random vector with a specified Gaussian distribution. Such a distribution may represent a collection of particles abidi…
Optimal control of the state statistics for a linear stochastic system
Yongxin Chen, Tryphon Georgiou, Michele Pavon
We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state di…
Optimal mass transport over bridges
Yongxin Chen, Tryphon Georgiou, Michele Pavon
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 generalizat…
Optimal transport over a linear dynamical system
Yongxin Chen, Tryphon Georgiou, Michele Pavon
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…