Related papers: On Simplifying Dependent Polyhedral Reductions
In this paper, we propose a stochastic Primal-Dual Hybrid Gradient (PDHG) approach for solving a wide spectrum of regularized stochastic minimization problems, where the regularization term is composite with a linear function. It has been…
Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a…
Regularization and data augmentation methods have been widely used and become increasingly indispensable in deep learning training. Researchers who devote themselves to this have considered various possibilities. But so far, there has been…
The common way to optimize auction and pricing systems is to set aside a small fraction of the traffic to run experiments. This leads to the question: how can we learn the most with the smallest amount of data? For truthful auctions, this…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…
This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…
The relaxation complexity $\mathrm{rc}(X)$ of the set of integer points $X$ contained in a polyhedron is the smallest number of facets of any polyhedron $P$ such that the integer points in $P$ coincide with $X$. It is a useful tool to…
We address the problem of \emph{convex optimization with dueling feedback}, where the goal is to minimize a convex function given a weaker form of \emph{dueling} feedback. Each query consists of two points and the dueling feedback returns a…
Individual-based models are complex and they have usually an elevated number of input parameters which must be tuned for reproducing the observed population data or the experimental results as accurately as possible. Thus, one of the…
A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…
Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to…
We formally introduce a systematic (de/re)-composition approach, based on the algebraic formalism of "Multi-Dimensional Homomorphisms (MDHs)". Our approach is designed as general enough to be applicable to a wide range of data-parallel…
This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and elementary computations and a corresponding…
Ensembling is a simple and popular technique for boosting evaluation performance by training multiple models (e.g., with different initializations) and aggregating their predictions. This approach is commonly reserved for the largest…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
Reducing the cognitive complexity of a piece of code to a given threshold is not trivial. Recently, we modeled software cognitive complexity reduction as an optimization problem and we proposed an approach to assist developers on this task.…
Approximating a convex function by a polyhedral function that has a limited number of facets is a fundamental problem with applications in various fields, from mitigating the curse of dimensionality in optimal control to bi-level…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…