The limitation of neural nets for approximation and optimization

We are interested in assessing the use of neural networks as surrogate models to approximate and minimize objective functions in optimization problems. While neural networks are widely used for machine learning tasks such as classification and regression, their application in solving optimization problems has been limited. Our study begins by determining the best activation function … Read more

A Single-Loop Algorithm for Decentralized Bilevel Optimization

Bilevel optimization has received more and more attention recently due to its wide applications in machine learning. In this paper, we consider bilevel optimization in decentralized networks. In particular, we propose a novel single-loop algorithm for solving decentralized bilevel optimization with strongly convex lower level problem. Our algorithm is fully single-loop and does not require … Read more

Mean–variance portfolio optimization with shrinkage estimation for recommender systems

This paper is concerned with a mean-variance portfolio optimization model with cardinality constraint for generating high-quality lists of recommendations. It is usually difficult to accurately estimate the rating covariance matrix required for mean-variance portfolio optimization because of a shortage of observed user ratings. To improve the accuracy of covariance matrix estimation, we apply shrinkage estimation … Read more

Analysis of a Class of Minimization Problems Lacking Lower Semicontinuity

The minimization of non-lower semicontinuous functions is a difficult topic that has been minimally studied. Among such functions is a Heaviside composite function that is the composition of a Heaviside function with a possibly nonsmooth multivariate function. Unifying a statistical estimation problem with hierarchical selection of variables and a sample average approximation of composite chance … Read more

An Integer Programming Approach To Subspace Clustering With Missing Data

In the Subspace Clustering with Missing Data (SCMD) problem, we are given a collection of n partially observed d-dimensional vectors. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal of SCMD is to cluster the vectors according to their subspace membership and recover the underlying basis, which can … Read more

Conjecturing-Based Discovery of Patterns in Data

We propose the use of a conjecturing machine that suggests feature relationships in the form of bounds involving nonlinear terms for numerical features and boolean expressions for categorical features. The proposed Conjecturing framework recovers known nonlinear and boolean relationships among features from data. In both settings, true underlying relationships are revealed. We then compare the … Read more

Learning the Follower’s Objective Function in Sequential Bilevel Games

We consider bilevel optimization problems in which the leader has no or only partial knowledge about the objective function of the follower. The studied setting is a sequential one in which the bilevel game is played repeatedly. This allows the leader to learn the objective function of the follower over time. We focus on two … Read more

Data-Driven Counterfactual Optimization For Personalized Clinical Decision-Making

Chronic diseases have a significant impact on global mortality rates and healthcare costs. Notably, machine learning-based clinical assessment tools are becoming increasingly popular for informing treatment targets for high-risk patients with chronic diseases. However, using these tools alone, it is challenging to identify personalized treatment targets that lower the risks of adverse outcomes to a … Read more

Almost-sure convergence of iterates and multipliers in stochastic sequential quadratic optimization

Stochastic sequential quadratic optimization (SQP) methods for solving continuous optimization problems with nonlinear equality constraints have attracted attention recently, such as for solving large-scale data-fitting problems subject to nonconvex constraints. However, for a recently proposed subclass of such methods that is built on the popular stochastic-gradient methodology from the unconstrained setting, convergence guarantees have been … Read more

Solution Path of Time-varying Markov Random Fields with Discrete Regularization

\(\) We study the problem of inferring sparse time-varying Markov random fields (MRFs) with different discrete and temporal regularizations on the parameters. Due to the intractability of discrete regularization, most approaches for solving this problem rely on the so-called maximum-likelihood estimation (MLE) with relaxed regularization, which neither results in ideal statistical properties nor scale to … Read more