相关论文: Randomized Transport Plans via Hierarchical Fully …

We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality…

The time-fractional optimal transport (OT) and mean-field planning (MFP) models are developed to describe the anomalous transport of the agents in a heterogeneous environment such that their densities are transported from the initial…

The robustness of fault detection algorithms against uncertainty is crucial in the real-world industrial environment. Recently, a new probabilistic design scheme called distributionally robust fault detection (DRFD) has emerged and received…

In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $\phi$-divergences and Wasserstein distances, respectively. While the former focuses on ambiguity in…

The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…

We propose a real-time decision framework for multimodal freight dispatch through a system of hierarchical hubs, using a probabilistic model for transit times. Instead of assigning a fixed time to each transit, we advocate using historical…

Optimal transport (OT) has become a natural framework for guiding the probability flows. Yet, the majority of recent generative models assume trivial geometry (e.g., Euclidean) and rely on strong density-estimation assumptions, yielding…

Routing problems such as Hamiltonian Path Problem (HPP), seeks a path to visit all the vertices in a graph while minimizing the path cost. This paper studies a variant, HPP with Probabilistic Terminals (HPP-PT), where each vertex has a…

We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…

We propose a data-driven portfolio selection model that integrates side information, conditional estimation and robustness using the framework of distributionally robust optimization. Conditioning on the observed side information, the…

Probabilistic sampling-based algorithms, such as the probabilistic roadmap (PRM) and the rapidly-exploring random tree (RRT) algorithms, represent one of the most successful approaches to robotic motion planning, due to their strong…

We present a novel probabilistic approach for optimal path experimental design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a…

Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…

Informative path planning algorithms are of paramount importance in applications like disaster management to efficiently gather information through a priori unknown environments. This is, however, a complex problem that involves finding a…

An important capability of autonomous multi-robot systems is to prevent collision among the individual robots. One approach to this problem is to plan conflict-free trajectories and let each of the robots follow its pre-planned trajectory.…

Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…

Balancing safety and efficiency when planning in crowded scenarios with uncertain dynamics is challenging where it is imperative to accomplish the robot's mission without incurring any safety violations. Typically, chance constraints are…

Optimal transport (OT) has enjoyed great success in machine learning as a principled way to align datasets via a least-cost correspondence, driven in large part by the runtime efficiency of the Sinkhorn algorithm (Cuturi, 2013). However,…

Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…

We propose dynamical optimal transport (OT) problems constrained in a parameterized probability subset. In application problems such as deep learning, the probability distribution is often generated by a parameterized mapping function. In…