Related papers: Mixed-Integer Convex Nonlinear Optimization with G…

Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…

Random forest and deep neural network are two schools of effective classification methods in machine learning. While the random forest is robust irrespective of the data domain, the deep neural network has advantages in handling high…

Most real-world classification problems deal with imbalanced datasets, posing a challenge for Artificial Intelligence (AI), i.e., machine learning algorithms, because the minority class, which is of extreme interest, often proves difficult…

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…

We study the problem of finding the optimal assortment that maximizes expected revenue under the decision forest model, a recently proposed nonparametric choice model that is capable of representing any discrete choice model and in…

Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

Clustering serves as a vital tool for uncovering latent data structures, and achieving both high accuracy and interpretability is essential. To this end, existing methods typically construct binary decision trees by solving mixed-integer…

Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…

We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…

Model performance is frequently reported only for the overall population under consideration. However, due to heterogeneity, overall performance measures often do not accurately represent model performance within specific subgroups. We…

Interpretability of reinforcement learning policies is essential for many real-world tasks but learning such interpretable policies is a hard problem. Particularly rule-based policies such as decision trees and rules lists are difficult to…

We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…

The integration of optimization problems within neural network architectures represents a fundamental shift from traditional approaches to handling constraints in deep learning. While it is long known that neural networks can incorporate…

In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…

When data have a hierarchical structure, such as students nested within classrooms, ignoring dependencies between observations can compromise the validity of imputation procedures. Standard tree-based imputation methods implicitly assume…

This paper proposes a new mixed-integer programming (MIP) formulation to optimize split rule selection in the decision tree induction process, and develops an efficient search algorithm that is able to solve practical instances of the MIP…

We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general…

A novel method called mixed variable system Monte Carlo tree search (MVSMCTS) formulation is presented for optimization problems considering various types of variables with single and mixed continuous-discrete system. This method utilizes a…