Related papers: No Cross-Validation Required: An Analytical Framew…

We demonstrate the ability of hybrid regularization methods to automatically avoid the double descent phenomenon arising in the training of random feature models (RFM). The hallmark feature of the double descent phenomenon is a spike in the…

While nowadays most gradient-based optimization methods focus on exploring the high-dimensional geometric features, the random error accumulated in a stochastic version of any algorithm implementation has not been stressed yet. In this…

We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…

Variable selection is an old and pervasive problem in regression analysis. One solution is to impose a lasso penalty to shrink parameter estimates toward zero and perform continuous model selection. The lasso-penalized mixture of linear…

We introduce a new convexified matching method for missing value imputation and individualized inference inspired by computational optimal transport. Our method integrates favorable features from mainstream imputation approaches: optimal…

We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…

This work proposes a novel method to generate C-Tests; a deviated form of cloze tests (a gap filling exercise) where only the last part of a word is turned into a gap. In contrast to previous works that only consider varying the gap size or…

We propose an ML-based model that automates and expedites the solution of MIPs by predicting the values of variables. Our approach is motivated by the observation that many problem instances share salient features and solution structures…

We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…

We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step…

We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

In this paper, we develop a new formulation of changeover constraints for mixed integer programming problem (MIP) that emerges in solving a short-term production scheduling problem. The new model requires fewer constraints than the original…

We consider the problem of minimizing an objective function that is the sum of a convex function and a group sparsity-inducing regularizer. Problems that integrate such regularizers arise in modern machine learning applications, often for…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…

In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation. Higher order regularity can be obtained via replacing the Laplacian regulariser with a…

Mixup - a neural network regularization technique based on linear interpolation of labeled sample pairs - has stood out by its capacity to improve model's robustness and generalizability through a surprisingly simple formalism. However, its…

In this paper, we develop a fast mixed-integer convex programming (MICP) framework for multi-robot navigation by combining graph attention networks and distributed optimization. We formulate a mixed-integer optimization problem for receding…

In fields such as autonomous and safety-critical systems, online optimization plays a crucial role in control and decision-making processes, often requiring the integration of continuous and discrete variables. These tasks are frequently…