Related papers: Adversarial Optimal Transport Through The Convolut…
The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…
Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation…
Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…
Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…
This paper proposes a novel mission planning algorithm for autonomous robots that selects an optimal waypoint sequence from a predefined set to maximize total reward while satisfying obstacle avoidance, state, input, derivative, mission…
Deep learning classifiers are now known to have flaws in the representations of their class. Adversarial attacks can find a human-imperceptible perturbation for a given image that will mislead a trained model. The most effective methods to…
We focus on establishing the foundational paradigm of a novel optimization theory based on convolution with convex kernels. Our goal is to devise a morally deterministic model of locating the global optima of an arbitrary function, which is…
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,…
We theoretically analyse the limits of robustness to test-time adversarial and noisy examples in classification. Our work focuses on deriving bounds which uniformly apply to all classifiers (i.e all measurable functions from features to…
Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…
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…
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
Conformal Prediction (CP) is a principled framework for quantifying uncertainty in blackbox learning models, by constructing prediction sets with finite-sample coverage guarantees. Traditional approaches rely on scalar nonconformity scores,…
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the…
We propose an algorithm using method of evolving junctions to solve the optimal path planning problems with piece-wise constant flow fields. In such flow fields with a convex Lagrangian in the objective function, we can prove that the…
We study the sample complexity of entropic optimal transport in high dimensions using computationally efficient plug-in estimators. We significantly advance the state of the art by establishing dimension-free, parametric rates for…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
The contribution of this paper is a generalized formulation of correctional learning using optimal transport, which is about how to optimally transport one mass distribution to another. Correctional learning is a framework developed to…