Related papers: Strong Formulations and Algorithms for Regularized…
Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…
Federated learning enables training on a massive number of edge devices. To improve flexibility and scalability, we propose a new asynchronous federated optimization algorithm. We prove that the proposed approach has near-linear convergence…
Randomized coordinate descent (RCD) is a popular optimization algorithm with wide applications in solving various machine learning problems, which motivates a lot of theoretical analysis on its convergence behavior. As a comparison, there…
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we…
In standard reinforcement learning (RL), a learning agent seeks to optimize the overall reward. However, many key aspects of a desired behavior are more naturally expressed as constraints. For instance, the designer may want to limit the…
Rotation averaging (RA) is a fundamental problem in robotics and computer vision. In RA, the goal is to estimate a set of $N$ unknown orientations $R_{1}, ..., R_{N} \in SO(3)$, given noisy measurements $R_{ij} \sim R^{-1}_{i} R_{j}$ of a…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
The optimal reactive power dispatch (ORPD) problem is an alternating current optimal power flow (ACOPF) problem where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are considered. The…
Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…
The parallel alternating direction method of multipliers (ADMM) algorithm is widely recognized for its effectiveness in handling large-scale datasets stored in a distributed manner, making it a popular choice for solving statistical…
Bayesian optimal experimental design (OED) seeks to conduct the most informative experiment under budget constraints to update the prior knowledge of a system to its posterior from the experimental data in a Bayesian framework. Such…
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…
We propose a new class of exact continuous relaxations of l0-regularized criteria involving non-quadratic data terms such as the Kullback-Leibler divergence and the logistic regression, possibly combined with an l2 regularization. We first…
The frequent directions (FD) technique is a deterministic approach for online sketching that has many applications in machine learning. The conventional FD is a heuristic procedure that often outputs rank deficient matrices. To overcome the…
We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
The Column Subset Selection Problem provides a natural framework for unsupervised feature selection. Despite being a hard combinatorial optimization problem, there exist efficient algorithms that provide good approximations. The drawback of…
We introduce implicit Deep Adaptive Design (iDAD), a new method for performing adaptive experiments in real-time with implicit models. iDAD amortizes the cost of Bayesian optimal experimental design (BOED) by learning a design policy…
This work investigates the geometry of a nonconvex reformulation of minimizing a general convex loss function $f(X)$ regularized by the matrix nuclear norm $\|X\|_*$. Nuclear-norm regularized matrix inverse problems are at the heart of many…