The paper proposes a distributionally robust regularization technique for mixed‑integer sparse programming models used in explainable machine learning. It extends recent DRO advances, traditionally applied to convex formulations, to mixed‑integer settings, offering statistical guarantees linked to a sparsity parameter. The method is demonstrated on binary classification models built from feature‑value rule sets.
arXiv:2306. 14851v5 Announce Type: replace-cross Abstract: Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner.
arXiv:2607. 00275v1 Announce Type: cross Abstract: Federated Learning (FL) is a distributed machine learning (ML) paradigm with collaboration among multiple clients without sharing data.
arXiv:2609.36310v1 Announce Type: new Abstract: Everywhere learning provides a principled framework for training AI models under constraints that must hold throughout the data distribution. In the du...
arXiv:2607. 03839v1 Announce Type: new Abstract: Sparse feature selection is critical for high-dimensional machine learning, yet traditional $\ell_1$-regularized methods are often brittle under observational noise and spurious correlations, leading to unstable feature supports and degraded generalization.
The paper introduces mixed integer linear programming (MILP) formulations for training sparse disjunctive normal form (DNF) networks, which are small networks with a conjunctive hidden layer and a disjunctive output layer. By fixing the network structure and optimizing weights, the authors achieve globally optimized rule sets that balance misclassification costs against sparsity. Their enhanced formulation reduces integer decision variables and redundant constraints, and a combined initialization and dropout approach breaks weight symmetries to promote diverse, stable rule representations, leading to improved computational efficiency and competitive accuracy on synthetic and UCI datasets.
arXiv:2610.02528v1 Announce Type: new Abstract: We introduce an autoregressive differentiable method to solve 0-1 integer programs. We fix an arbitrary order of the binary variables and we train a tr...
arXiv:2609. 19077v1 Announce Type: cross Abstract: Formal explainability provides mathematically grounded justifications for individual predictions.
The paper introduces a distributionally robust method for learning hyperparameters of first‑order convex optimization algorithms. By minimizing a Wasserstein‑robust performance estimation problem over a dataset of problem instances, the approach interpolates between classical learning‑to‑optimize (L2O) and worst‑case PEP design. The authors solve the resulting problem with stochastic gradient descent, provide high‑probability risk bounds, and demonstrate that the learned algorithms outperform both worst‑case optimal and vanilla L2O baselines on logistic regression, LASSO, and linear programming tasks.
arXiv:2605.28165v2 Announce Type: replace Abstract: Robust learning methods such as distributionally robust optimization, vicinal risk minimization, Mixup, and label smoothing address different sourc...
CG4AI is a column generation framework that trains AI models while enforcing linear constraints on their outputs. It constructs a convex combination of models, using a master linear program to set mixture weights and a pricing subproblem to generate new models guided by dual variables, focusing on the most violated constraints. The method is applied to MNIST digit classification—demonstrating constraint learning, adversarial robustness, error correction, and output relabeling—and to multi‑commodity flow routing, achieving feasible predictors with higher accuracy than single‑model baselines.
The paper introduces ReMILP, a reformulation‑contrastive learning framework that uses self‑supervision from equivalent formulations of mixed‑integer linear programs (MILPs). By distinguishing re‑descriptions and substitutions, the method trains a graph neural network and a hypernetwork to predict how variable embeddings transform under changes of variables, achieving invariance and equivariance without solver‑derived labels. The learned representations prove useful for tasks such as binary solution, constraint activity, and integrality gap prediction, and serve as a strong initialization for fine‑tuning.
The paper investigates binary classification with abstention under separate class‑conditional error constraints, aiming to minimize abstention while keeping both error types below specified thresholds. It derives the distribution‑free minimax rate of excess abstention risk, introduces surrogate‑loss formulations for computational feasibility with models like neural networks, and provides finite‑sample guarantees for excess surrogate ambiguity risk. The authors also formulate the learning task as a constrained optimization problem, analyze its computational complexity in the convex setting, and empirically evaluate the approach against a competing method on several datasets.