相关论文: PDOT: a Practical Primal-Dual Algorithm and a GPU-…

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 Unbalanced Optimal Transport (UOT) problem plays increasingly important roles in computational biology, computational imaging and deep learning. Scaling algorithm is widely used to solve UOT due to its convenience and good convergence…

Quadratic cone programs are rapidly becoming the standard canonical form for convex optimization problems. In this paper we address the question of differentiating the solution map for such problems, generalizing previous work for linear…

We propose unified data structures and algorithms for free-surface fluid simulations based on partial optimal transport, such as the Power Particles method or Gallou\"et-M\'erigot's scheme. Such methods previously relied on a discretization…

In the last fifteen years a significant progress was achieved by considering an entropic relaxation of the classical multi-partite optimal transport problem (MPOTP). The entropic relaxation gives rise to the rescaling problem of a given…

The Sinkhorn algorithm is a widely used method for solving the optimal transport problem, and the Greenkhorn algorithm is one of its variants. While there are modified versions of these two algorithms whose computational complexities are…

This paper introduces a novel Model Predictive Control (MPC) implementation for legged robot locomotion that leverages GPU parallelization. Our approach enables both temporal and state-space parallelization by incorporating a parallel…

We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $\mu$ is transported to a discrete target measure $\nu$, with particular attention to the OT map approximation. In this setting, Stochastic…

\emph{Optimal Transport} (OT) has emerged as an important computational tool in machine learning and computer vision, providing a geometrical framework for studying probability measures. OT unfortunately suffers from the curse of…

While the optimal transport (OT) problem was originally formulated as a linear program, the addition of entropic regularization has proven beneficial both computationally and statistically, for many applications. The Sinkhorn fixed-point…

Unbalanced optimal transport (UOT) extends optimal transport (OT) to take into account mass variations to compare distributions. This is crucial to make OT successful in ML applications, making it robust to data normalization and outliers.…

We consider the one-to-one Pickup and Delivery Problem (PDP) in Euclidean Space with arbitrary dimension $d$ where $n$ transportation requests are picked i.i.d. with a separate origin-destination pair for each object to be moved. First, we…

In many machine learning applications, it is necessary to meaningfully aggregate, through alignment, different but related datasets. Optimal transport (OT)-based approaches pose alignment as a divergence minimization problem: the aim is to…

Conventional online multi-task learning algorithms suffer from two critical limitations: 1) Heavy communication caused by delivering high velocity of sequential data to a central machine; 2) Expensive runtime complexity for building task…

The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to…

In this work we propose a batch version of the Greenkhorn algorithm for multimarginal regularized optimal transport problems. Our framework is general enough to cover, as particular cases, some existing algorithms like Sinkhorn and…

We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…

Conventional Public Transport (PT) is based on fixed lines, running with routes and schedules determined a-priori. In low-demand areas, conventional PT is inefficient. Therein, Mobility on Demand (MoD) could serve users more efficiently and…

We consider the all-pairs multicommodity network flow problem on a network with capacitated edges. The usual treatment keeps track of a separate flow for each source-destination pair on each edge; we rely on a more efficient formulation in…