Related papers: Optimizing the expected maximum of two linear func…
We consider a generic empirical composition optimization problem, where there are empirical averages present both outside and inside nonlinear loss functions. Such a problem is of interest in various machine learning applications, and…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…
We introduce Network Maximal Correlation (NMC) as a multivariate measure of nonlinear association among random variables. NMC is defined via an optimization that infers transformations of variables by maximizing aggregate inner products…
In this paper we consider a distributed optimization scenario in which the aggregate objective function to minimize is partitioned, big-data and possibly non-convex. Specifically, we focus on a set-up in which the dimension of the decision…
In this paper we examine problems motivated by on-line financial problems and stochastic games. In particular, we consider a sequence of entirely arbitrary distinct values arriving in random order, and must devise strategies for selecting…
Dual feasible functions (DFFs) have been used to provide bounds for standard packing problems and valid inequalities for integer optimization problems. In this paper, the connection between general DFFs and a particular family of…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
Variational Optimization forms a differentiable upper bound on an objective. We show that approaches such as Natural Evolution Strategies and Gaussian Perturbation, are special cases of Variational Optimization in which the expectations are…
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…
We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect…
We use a rank one Gaussian perturbation to derive a smooth stochastic approximation of the maximum eigenvalue function. We then combine this smoothing result with an optimal smooth stochastic optimization algorithm to produce an efficient…
Diffusion on complex networks is often modeled as a stochastic process. Yet, recent work on strategic diffusion emphasizes the decision power of agents and treats diffusion as a strategic problem. Here we study the computational aspects of…
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with…
This paper considers stochastic optimization problems whose objective functions involve powers of random variables. For example, consider the classic Stochastic lp Load Balancing Problem (SLBp): There are $m$ machines and $n$ jobs, and…
This paper studies a distributed stochastic optimization problem over random networks with imperfect communications subject to a global constraint, which is the intersection of local constraint sets assigned to agents. The global cost…