Related papers: Adaptive Approximation for Multivariate Linear Pro…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
We present adaptive sequential SAA (sample average approximation) algorithms to solve large-scale two-stage stochastic linear programs. The iterative algorithm framework we propose is organized into \emph{outer} and \emph{inner} iterations…
We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…
Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algorithms are guaranteed to provide answers that satisfy a…
In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…
In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…
In this paper, we revisit the distributed coverage control problem with multiple robots on both metric graphs and in non-convex continuous environments. Traditionally, the solutions provided for this problem converge to a locally optimal…
In recent years, many design automation methods have been developed to routinely create approximate implementations of circuits and programs that show excellent trade-offs between the quality of output and required resources. This paper…
Adversarial training can be used to learn models that are robust against perturbations. For linear models, it can be formulated as a convex optimization problem. Compared to methods proposed in the context of deep learning, leveraging the…
This paper deals with nonconvex stochastic optimization problems in deep learning and provides appropriate learning rates with which adaptive learning rate optimization algorithms, such as Adam and AMSGrad, can approximate a stationary…
The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to…
In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some…
We build a theoretical framework for designing and understanding practical meta-learning methods that integrates sophisticated formalizations of task-similarity with the extensive literature on online convex optimization and sequential…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
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…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…