Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine learning, as gradient-based algorithms built on the implicit function reformulation have enabled the computation of large-scale problems involving possibly millions of variables. Despite … Read more
Stochastic minimax problems with decision-dependent distributions (SMDD) have emerged as a crucial framework for modeling complex systems where data distributions drift in response to decision variables. Most existing methods for SMDD rely on an explicit functional relationship between the decision variables and the probability distribution. In this paper, we propose two sample-based zeroth-order algorithms, namely … Read more
A stochastic program typically involves several parameters, including deterministic first-stage parameters and stochastic second-stage elements that serve as input data. These programs are re-solved whenever any input parameter changes. However, in practical applications, quick decision-making is necessary, and solving a stochastic program from scratch for every change in input data can be computationally costly. This … Read more
A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on a convex set to the use of both a stochastic gradient and a possibly inexact projection map. Under standard assumptions in the field of stochastic gradient methods, we provide theoretical … Read more
In model extraction attacks, the goal is to reveal the parameters of a black-box machine learning model by querying the model for a selected set of data points. Due to an increasing demand for explanations, this may involve counterfactual queries besides the typically considered factual queries. In this work, we consider linear models and three … Read more
In this paper, we introduce a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution by developing interpretable and tractable decision rules that prescribe decisions using covariates. We first introduce the causal Sinkhorn discrepancy (CSD), an entropy-regularized causal Wasserstein distance that encourages continuous transport plans while … Read more
This work presents a novel optimization approach for training linear classifiers in multiclass classification tasks, when focusing on a regularized and smooth Weston-Watkins support vector machine (SVM) model. We propose a Majorization-Minimization (MM) algorithm to solve the resulting, Lipschitz-differentiable, optimization problem. To enhance scalability of the algorithm when tackling large datasets, we introduce an incremental … Read more
Convex maximization encompasses a broad class of optimization problems and is generally NP-hard, even for low-rank objectives. This paper investigates structural conditions under which convex maximization becomes polynomially solvable. From a geometric perspective, we introduce comonotonicity, a structural property of the feasible region crucial for problem tractability, and establish mathematical characterizations of this property. Under comonotonicity and … Read more
We introduce method iR2N, a modified proximal quasi-Newton method for minimizing the sum of a \(C^1\) function \(f\) and a lower semi-continuous prox-bounded \(h\) that permits inexact evaluations of \(f\), \(\nabla f\) and of the relevant proximal operators. Both \(f\) and \(h\) may be nonconvex. In applications where the proximal operator of \(h\) is not … Read more
The tractability of optimization problems depends critically on structural properties of the objective function. Convexity guarantees global optimality of local solutions and enables polynomial-time algorithms under mild assumptions, but many problems arising in modern applications—particularly in machine learning—are inherently nonconvex. Remarkably, a large class of such problems remains amenable to efficient optimization due to additional … Read more