Related papers: Walks on hyperplane arrangements and optimization …
Several recent applications of optimal transport (OT) theory to machine learning have relied on regularization, notably entropy and the Sinkhorn algorithm. Because matrix-vector products are pervasive in the Sinkhorn algorithm, several…
In contrast to the many continuous global optimization methods that assume the objective function and constraints are factorable, we study how to find globally maximal solutions to problems that are not factorable, focusing on a particular…
The performance of industrial robotic work cells depends on optimizing various hyperparameters referring to the cell layout, such as robot base placement, tool placement, and kinematic design. Achieving this requires a bilevel optimization…
We introduce a stochastic global optimization method based on random walks on Grassmannian manifolds. To minimize a continuous objective $\ell:\mathbb{R}^d\rightarrow\mathbb{R}$, the method repeatedly samples random $k$-dimensional linear…
We study the asymptotic behaviour of the most likely trajectories of a planar random walk that result in large deviations of the area of their convex hull. If the Laplace transform of the increments is finite on $R^2$, such a scaled limit…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
We develop a numerical method for the martingale analogue of the Benamou--Brenier optimal transport problem, which seeks a martingale interpolating two prescribed marginals which is closest to the Brownian motion. Recent contributions have…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
A large number of problems in computer vision can be modelled as energy minimization problems in a Markov Random Field (MRF) or Conditional Random Field (CRF) framework. Graph-cuts based $\alpha$-expansion is a standard move-making method…
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,…
In order to solve complex, long-horizon tasks, intelligent robots need to carry out high-level, abstract planning and reasoning in conjunction with motion planning. However, abstract models are typically lossy and plans or policies computed…
Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes. If only…
We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…
In this paper, a reduced-rank scheme with joint iterative optimization is presented for direction of arrival estimation. A rank-reduction matrix and an auxiliary reduced-rank parameter vector are jointly optimized to calculate the output…
In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy…
Motivated by the success of Sinkhorn's algorithm for entropic optimal transport, we study convergence properties of iterative proportional fitting procedures (IPFP) used to solve more general information projection problems. We establish…
Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…