Related papers: Probing to Minimize
An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…
We study the problem of optimal traffic prediction and monitoring in large-scale networks. Our goal is to determine which subset of K links to monitor in order to "best" predict the traffic on the remaining links in the network. We consider…
In this paper, we present a unified analysis of both convergence and optimality of adaptive mixed finite element methods for a class of problems when the finite element spaces and corresponding a posteriori error estimates under…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. While these models have been quite popular, the solutions Constrained submodular function…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with a {\color{black} functional or expectation} constraint on either decision variables or problem parameters. We first present a new…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…
We provide a unifying approximate dynamic programming framework that applies to a broad variety of problems involving sequential estimation. We consider first the construction of surrogate cost functions for the purposes of optimization,…
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…
$ $In many optimization problems, a feasible solution induces a multi-dimensional cost vector. For example, in load-balancing a schedule induces a load vector across the machines. In $k$-clustering, opening $k$ facilities induces an…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
Minimax optimization plays a key role in adversarial training of machine learning algorithms, such as learning generative models, domain adaptation, privacy preservation, and robust learning. In this paper, we demonstrate the failure of…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
We present combinatorial and parallelizable algorithms for maximization of a submodular function, not necessarily monotone, with respect to a size constraint. We improve the best approximation factor achieved by an algorithm that has…
This paper explores adaptive variance reduction methods for stochastic optimization based on the STORM technique. Existing adaptive extensions of STORM rely on strong assumptions like bounded gradients and bounded function values, or suffer…
In this paper, we develop fast algorithms for two stochastic submodular maximization problems. We start with the well-studied adaptive submodular maximization problem subject to a cardinality constraint. We develop the first linear-time…
Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…