Related papers: A First-Order Algorithm for the A-Optimal Experime…
We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First,…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
This research addresses the multiprocessor scheduling problem of hard real-time systems, and it especially focuses on optimal and global schedulers when practical constraints are taken into account. First, we propose an improvement of the…
We study constrained stochastic programs where the decision vector at each time slot cannot be chosen freely but is tied to the realization of an underlying random state vector. The goal is to minimize a general objective function subject…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
Significant advances in edge computing capabilities enable learning to occur at geographically diverse locations. In general, the training data needed in those learning tasks are not only heterogeneous but also not fully generated locally.…
This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first consider a distributed first-order primal-dual…
We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
Algorithms which compute locally optimal continuous designs often rely on a finite design space or on repeatedly solving a complex non-linear program. Both methods require extensive evaluations of the Jacobian Df of the underlying model.…
In this paper, we study the sampling problem for first-order logic proposed recently by Wang et al. -- how to efficiently sample a model of a given first-order sentence on a finite domain? We extend their result for the…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
One of the beauties of the projected gradient descent method lies in its rather simple mechanism and yet stable behavior with inexact, stochastic gradients, which has led to its wide-spread use in many machine learning applications.…
The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the…
A framework is developed for applying accelerated methods to general hyperbolic programming, including linear, second-order cone, and semidefinite programming as special cases. The approach replaces a hyperbolic program with a convex…
The Frank-Wolfe (FW) method is a popular approach for solving optimization problems with structured constraints that arise in machine learning applications. In recent years, stochastic versions of FW have gained popularity, motivated by…
We develop $D$-optimal designs for linear models with first-order interactions on a subset of the $2^K$ full factorial design region, when both the number of factors set to the higher level and the number of factors set to the lower level…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…