相关论文: Approximate Vanishing Ideal Computations at Scale

Frequently, when dealing with many machine learning models, optimization problems appear to be challenging due to a limited understanding of the constructions and characterizations of the objective functions in these problems. Therefore,…

Automatic differentiation variational inference (ADVI) offers fast and easy-to-use posterior approximation in multiple modern probabilistic programming languages. However, its stochastic optimizer lacks clear convergence criteria and…

Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…

This paper considers nonsmooth convex optimization with either a subgradient or proximal operator oracle. In both settings, we identify algorithms that achieve the recently introduced game-theoretic optimality notion for algorithms known as…

Markov decision processes (MDPs) are used to model stochastic systems in many applications. Several efficient algorithms to compute optimal policies have been studied in the literature, including value iteration (VI) and policy iteration.…

We study the unconstrained minimization of a smooth and strongly convex population loss function under a stochastic oracle that introduces both additive and multiplicative noise; this is a canonical and widely-studied setting that arises…

We propose a self-improving algorithm for computing Voronoi diagrams under a given convex distance function with constant description complexity. The $n$ input points are drawn from a hidden mixture of product distributions; we are only…

Amortized variational inference is an often employed framework in simulation-based inference that produces a posterior approximation that can be rapidly computed given any new observation. Unfortunately, there are few guarantees about the…

With the growing practical interest in vision-based tasks for autonomous systems, the need for efficient and complex methods becomes increasingly larger. In the rush to develop new methods with the aim to outperform the current state of the…

This paper focuses on optimization problems constrained by Parametric Variational Inequalities (PVI) defined on a moving set. Unlike most existing works on mathematical programs with equilibrium constraints, the equilibrium constraints have…

We consider stochastic approximation for the least squares regression problem in the non-strongly convex setting. We present the first practical algorithm that achieves the optimal prediction error rates in terms of dependence on the noise…

We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…

Deep neural networks have reshaped modern machine learning by learning powerful latent representations that often align with the manifold hypothesis: high-dimensional data lie on lower-dimensional manifolds. In this paper, we establish a…

We study inverse optimization (IO), where the goal is to use a parametric optimization program as the hypothesis class to infer relationships between input-decision pairs. Most of the literature focuses on learning only the objective…

We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex function whose subgradients are estimated under heavy-tailed noise. Existing work often employs…

We propose an orthogonal approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model with general rotationally invariant (RI) noise. We establish a rigorous state evolution that exactly…

We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With $O(r^3 \kappa^2 n \log n)$ random…

In modeling physical systems it is sometimes useful to construct border bases of 0-dimensional polynomial ideals which are contained in the ideal generated by a given set of polynomials. We define and construct such subideal border bases,…

We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed…