Related papers: Remarks on multi-period martingale optimal transpo…
We study a stochastic control problem for continuous multidimensional martingales with fixed quadratic variation. In a radially symmetric environment, we are able to find an explicit solution to the control problem and find an optimal…
Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
We address the problem of adapting robot trajectories to improve safety, comfort, and efficiency in human-robot collaborative tasks. To this end, we propose CoMOTO, a trajectory optimization framework that utilizes stochastic motion…
An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of…
We consider the numerical solution of the discrete multi-marginal optimal transport (MOT) by means of the Sinkhorn algorithm. In general, the Sinkhorn algorithm suffers from the curse of dimensionality with respect to the number of…
We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times of Brownian motion subject to the constraint that the distribution of the stopping time is a…
Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…
We establish structural properties of optimal stopping problems under time-consistent dynamic (coherent) risk measures, focusing on value function monotonicity and the existence of control limit (threshold) optimal policies. While such…
We propose an optimal solution to a deterministic dynamic assignment problem by leveraging connections to the theory of discrete optimal transport to convert the combinatorial assignment problem into a tractable linear program. We seek to…
Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover…
We study the problem of optimal multi-robot path planning on graphs (MPP) over four distinct minimization objectives: the total arrival time, the makespan (last arrival time), the total distance, and the maximum (single-robot traveled)…
The optimal (Monge-Kantorovich) transportation problem is discussed from several points of view. The Lagrangian formulation extends the action of the {\em Lagrangian} $L(v,x,t)$ from the set of orbits in $\R^n$ to a set of measure-valued…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
The paper outlines novel variational technique for finding microstructures of optimal multimaterial composites, bounds of composites properties, and multimaterial optimal designs. The translation method that is used for the exact…
Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…
In this work, we present an approach to minimizing the time necessary for the end-effector of a redundant robot manipulator to traverse a Cartesian path by optimizing the trajectory of its joints. Each joint has limits in the ranges of…
We introduce Hierarchical Jump multi-marginal transport (HJMOT), a generalization of multi-marginal optimal transport where mass can "jump" over intermediate spaces via augmented isolated points. Established on Polish spaces, the framework…