Our project investigates replacing the classical adversarial discriminator in GAN training with a kernel-based distance metric, namely Kernel Stein Discrepancy (KSD). We assess whether a kernelized objective can improve training stability and efficiency without compromising sample quality, and we evaluate accelerated Nystrom approximations with Renyi landmark selection on CIFAR-10. ArticleDownload View PDF
A new Block Coordinate Gradient (BCG) method, dubbed bAdag, for smooth, nonconvex minimization problem is proposed; it falls in the class of Objective Function Free Optimization (OFFO) methods, and it is based on the AdaGrad algorithm. At each iteration, our method computes an adaptive step size based on the cumulative sum of block gradients, instead … Read more
Variable projection is a classical technique for separable nonlinear least-squares problems, in which variables that enter linearly are eliminated exactly, yielding a reduced nonlinear problem. By expressing this framework as a particular instance of a broader class of bilevel optimization problems, we develop a constrained variable-projection framework for data-science models, where the remaining variables are … Read more
Modern experimentation in business and public policy often studies targeted interventions whose effects depend on the heterogeneous attributes of individuals. We examine heterogeneous treatment effects through the lens of optimal design of experiments, which allocates treatment decisions to maximize the precision of estimated treatment-covariate interactions. We introduce the D-optimal partitioning problem for balancing the information … Read more
A new class of asynchronous adaptive first-order optimization methods is introduced, comprising asynchronous variants of several popular algorithms. Versions of these methods using momentum and/or inexact normalization are also considered. The convergence of methods in the class on non-convex functions is analyzed in a fully stochastic setting, and is shown to be (up to logarithmic … Read more
Distributionally robust optimization (DRO) provides a principled framework for decision-making under distributional uncertainty. Classical data-driven DRO frameworks typically construct ambiguity sets from distributional information, such as moment constraints, divergence neighborhoods, or Wasserstein balls, specified before the downstream loss is considered. We propose a task-aware DRO framework based on targeted integral probability metrics. The ambiguity set … Read more
We design a class of additive noise mechanisms that satisfy \((\varepsilon, \delta)\)-differential privacy (DP) for scalar, real-valued query functions with known sensitivities, with a particular focus on moderate and low-privacy regimes. These mechanisms, which we call \textit{mixture mechanisms}, are constructed by mixing multiple Gaussian distributions that share the same variance but differ in their means … Read more
Dynamic dispatch networks in logistics and transportation require real-time, constraint-aware decision-making under stochastic demand. This paper bridges mathematical optimization, optimal control theory, and reinforcement learning by establishing non-asymptotic theoretical guarantees for learning-based optimal control in constrained stochastic dispatch systems. We formulate the problem as a constrained Markov decision process, enforce feasibility via a projection-based policy … Read more
A unified framework for first-order optimization algorithms for nonconvex unconstrained optimization is proposed that uses adaptively preconditioned gradients and includes popular methods such as full and diagonal AdaGrad, AdaNorm, as well as an adpative variants of Muon. This framework also allows combining heterogeneous geometries across different groups of variables while preserving a unified convergence analysis. … Read more
This paper addresses the challenge of enhancing public policy decision-making by efficiently solving principal-agent models (PAMs) for public-private partnerships, a critical yet computationally demanding problem. We develop a fast, interpretable, and generalizable approach to support policy decisions under these settings. We propose an interpretable ensemble heuristic (EH) that integrates Machine Learning (ML), Operations Research (OR), … Read more