相关论文: Differentiable Cost-Parameterized Monge Map Estima…

The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dimensional space) is a crucial problem arising in the…

Autonomous navigation in off-road environments remains a significant challenge in field robotics, particularly for Unmanned Ground Vehicles (UGVs) tasked with search and rescue, exploration, and surveillance. Effective long-range planning…

We consider Kantorovich optimal transportation problem in the case where the cost function and marginal distributions continuously depend on a parameter with values in a metric space. We prove the existence of approximate optimal Monge…

Traversing terrain with good traction is crucial for achieving fast off-road navigation. Instead of manually designing costs based on terrain features, existing methods learn terrain properties directly from data via self-supervision to…

The process of designing costmaps for off-road driving tasks is often a challenging and engineering-intensive task. Recent work in costmap design for off-road driving focuses on training deep neural networks to predict costmaps from sensory…

Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…

In this paper, we address the problem of adaptive path planning for accurate semantic segmentation of terrain using unmanned aerial vehicles (UAVs). The usage of UAVs for terrain monitoring and remote sensing is rapidly gaining momentum due…

In this work we introduce an implementation for which machine learning techniques helped improve the overall performance of an evolutionary algorithm for an optimization problem, namely a variation of robust minimum-cost path in graphs. In…

We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…

Unbalanced optimal transport (UOT) extends classical optimal transport to measures with different total masses, but statistical guarantees for Monge-type estimation remain limited. We study unbalanced transport with quadratic cost and…

In this paper we propose a novel end-to-end learnable network that performs joint perception, prediction and motion planning for self-driving vehicles and produces interpretable intermediate representations. Unlike existing neural motion…

Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. OT, however, is very sensitive to outliers (samples with large noise) in the data since in its objective function,…

Autonomous navigation in off-road conditions requires an accurate estimation of terrain traversability. However, traversability estimation in unstructured environments is subject to high uncertainty due to the variability of numerous…

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…

Optimal path planning requires finding a series of feasible states from the starting point to the goal to optimize objectives. Popular path planning algorithms, such as Effort Informed Trees (EIT*), employ effort heuristics to guide the…

We introduce \emph{in-context operator learning on probability measure spaces} for optimal transport (OT). The goal is to learn a single solution operator that maps a pair of distributions to the OT map, using only few-shot samples from…

We develop a general condition on the cost function which is sufficient to imply Monge solution and uniqueness results in the multi-marginal optimal transport problem. This result unifies and generalizes several results in the rather…

Matching a source to a target probability measure is often solved by instantiating a linear optimal transport (OT) problem, parameterized by a ground cost function that quantifies discrepancy between points. When these measures live in the…

Robots are frequently tasked to gather relevant sensor data in unknown terrains. A key challenge for classical path planning algorithms used for autonomous information gathering is adaptively replanning paths online as the terrain is…

We propose a novel locally adaptive learning estimator for enhancing the inter- and intra- discriminative capabilities of Deep Neural Networks, which can be used as improved loss layer for semantic image segmentation tasks. Most loss layers…