Related papers: Control, Transport and Sampling: Towards Better Lo…
Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value function estimate and identifies the part of the state space…
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…
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 present a stochastic optimal control problem for a tree network. The dynamics of the network are governed by transport equations with a special emphasis on the non-linear damping function. Demand profiles at the network sinks are…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
This paper exploit the equivalence between the Schr\"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a…
For a nonlinear stochastic path planning problem, sampling-based algorithms generate thousands of random sample trajectories to find the optimal path while guaranteeing safety by Lagrangian penalty methods. However, the sampling-based…
This article is aimed at presenting the Schr\"odinger problem and some of its connections with optimal transport. We hope that it can be used as a basic user's guide to Schr\"odinger problem. We also give a survey of the related literature.…
The bridge problem is to find an SDE (or sometimes an ODE) that bridges two given distributions. The application areas of the bridge problem are enormous, among which the recent generative modeling (e.g., conditional or unconditional image…
Diffusion and flow-matching have emerged as powerful methodologies for generative modeling, with remarkable success in capturing complex data distributions and enabling flexible guidance at inference time. Many downstream applications,…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…
Diffusion Bridge and Flow Matching have both demonstrated compelling empirical performance in transformation between arbitrary distributions. However, there remains confusion about which approach is generally preferable, and the substantial…
We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for…
We compare several approaches to learn an Optimal Map, represented as a neural network, between probability distributions. The approaches fall into two categories: ``Heuristics'' and approaches with a more sound mathematical justification,…
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…
Alongside optimization-based planners, sampling-based approaches are often used in trajectory planning for autonomous driving due to their simplicity. Model predictive path integral control is a framework that builds upon optimization…
It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal…