Related papers: Dual Representation of Minimum Divergence Under In…
Methods that align distributions by minimizing an adversarial distance between them have recently achieved impressive results. However, these approaches are difficult to optimize with gradient descent and they often do not converge well…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve first fitting non-parametric regression models…
The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial…
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
In the contextual linear bandit setting, algorithms built on the optimism principle fail to exploit the structure of the problem and have been shown to be asymptotically suboptimal. In this paper, we follow recent approaches of deriving…
We introduce and study Minimum Cut Representability, a framework to solve optimization and feasibility problems over stable matchings by representing them as minimum s-t cut problems on digraphs over rotations. We provide necessary and…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…
We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes…
Duality is a foundational tool in robust and distributionally robust optimization (RO and DRO), underpinning both analytical insights and tractable reformulations. The prevailing approaches in the literature primarily rely on saddle-point…
This paper presents the Lagrangian duality theory for mixed-integer semidefinite programming (MISDP). We derive the Lagrangian dual problem and prove that the resulting Lagrangian dual bound dominates the bound obtained from the continuous…
We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first…
In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
This paper is focused on $f$-divergences, consisting of three main contributions. The first one introduces integral representations of a general $f$-divergence by means of the relative information spectrum. The second part provides a new…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…
Given a dataset of points in a metric space and an integer $k$, a diversity maximization problem requires determining a subset of $k$ points maximizing some diversity objective measure, e.g., the minimum or the average distance between two…