Related papers: Improved Linear Programs for Discrete Barycenters
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…
Computational implementation of optimal transport barycenters for a set of target probability measures requires a form of approximation, a widespread solution being empirical approximation of measures. We provide an $O(\sqrt{N/n})$…
Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances…
The optimal control input for linear systems can be solved from algebraic Riccati equation (ARE), from which it remains questionable to get the form of the exact solution. In engineering, the acceptable numerical solutions of ARE can be…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of…
It is well-known that proper scaling can increase the efficiency of computational problems. In this paper we define and show that a balancing technique can substantially improve the computational efficiency of optimal control algorithms. We…
Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and…
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…
We propose a flexible gradient-based framework for learning linear programs from optimal decisions. Linear programs are often specified by hand, using prior knowledge of relevant costs and constraints. In some applications, linear programs…
Aggregating data from multiple sources can be formalized as an Optimal Transport (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, in real-world scenarios,…
We propose a stronger formulation of the precedence constraints and the station limits for the simple assembly line balancing problem. The linear relaxation of the improved integer program theoretically dominates all previous formulations…
Optimal transport is a notoriously difficult problem to solve numerically, with current approaches often remaining intractable for very large scale applications such as those encountered in machine learning. Wasserstein barycenters -- the…
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…
Linear models are used in online decision making, such as in machine learning, policy algorithms, and experimentation platforms. Many engineering systems that use linear models achieve computational efficiency through distributed systems…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…