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We propose a discrete time formulation of the semi martingale optimal transport problembased on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by Guo et…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
Line planning in public transport is the strategic problem of selecting lines and their operating frequencies. This problem is important as it defines the passenger service, based on available connections and expected travel times, and…
Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…
Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-like algorithms for computing optimal transport plans. However,…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
Multimarginal Optimal Transport (MOT) has attracted significant interest due to applications in machine learning, statistics, and the sciences. However, in most applications, the success of MOT is severely limited by a lack of efficient…
This paper proposes an efficient HOT algorithm for solving the optimal transport (OT) problems with finite supports. We particularly focus on an efficient implementation of the HOT algorithm for the case where the supports are in…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…
The dynamic formulation of optimal transport has attracted growing interests in scientific computing and machine learning, and its computation requires to solve a PDE-constrained optimization problem. The classical Eulerian discretization…
Many real-world problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns in the field of computer vision. Recently, the alignment problem…
We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This…
Wasserstein GANs with Gradient Penalty (WGAN-GP) are a very popular method for training generative models to produce high quality synthetic data. While WGAN-GP were initially developed to calculate the Wasserstein 1 distance between…
For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the Armijo line search for global convergence. Such existing…
We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case…
Optimal Transport is a popular distance metric for measuring similarity between distributions. Exact algorithms for computing Optimal Transport can be slow, which has motivated the development of approximate numerical solvers (e.g. Sinkhorn…
Applications such as adversarially robust training and Wasserstein Distributionally Robust Optimization (WDRO) can be naturally formulated as min-sum-max optimization problems. While this formulation can be rewritten as an equivalent…