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Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
This paper investigates the control of nonlinear systems using a piecewise linear approximation framework. The proposed approach combines a PID controller with locally linearized models obtained by partitioning the nonlinear function into…
In this paper we study nonconvex and nonsmooth optimization problems with semi-algebraic data, where the variables vector is split into several blocks of variables. The problem consists of one smooth function of the entire variables vector…
In this paper, by employing the asymptotic expansion method, we prove the existence and uniqueness of a smoothing solution for a time-dependent nonlinear singularly perturbed partial differential equation (PDE) with a small-scale parameter.…
Fine-tuning all parameters of Large Language Models (LLMs) is computationally expensive. Parameter-Efficient Fine-Tuning (PEFT) methods address this by selectively fine-tuning specific parameters. Most of the parameter efficient fine-tuning…
We introduce SPRING, a novel stochastic proximal alternating linearized minimization algorithm for solving a class of non-smooth and non-convex optimization problems. Large-scale imaging problems are becoming increasingly prevalent due to…
This paper advocates a new paradigm Personalized Empirical Risk Minimization (PERM) to facilitate learning from heterogeneous data sources without imposing stringent constraints on computational resources shared by participating devices. In…
We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging…
In [1], the distributed linear-quadratic problem with fixed communication topology (DFT-LQ) and the sparse feedback LQ problem (SF-LQ) are formulated into a nonsmooth and nonconvex optimization problem with affine constraints. Moreover, a…
We study the differentially private (DP) empirical risk minimization (ERM) problem under the semi-sensitive DP setting where only some features are sensitive. This generalizes the Label DP setting where only the label is sensitive. We give…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM…
Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…
We propose a novel unsupervised framework for \emph{Invariant Risk Minimization} (IRM), extending the concept of invariance to settings where labels are unavailable. Traditional IRM methods rely on labeled data to learn representations that…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
We prove the applicability of the Weighted Energy-Dissipation (WED) variational principle [50] to nonlinear parabolic stochastic partial differential equations in abstract form. The WED principle consists in the minimization of a…
State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics,…
Optimization problems over discrete or quantized variables are very challenging in general due to the combinatorial nature of their search space. Piecewise-affine regularization (PAR) provides a flexible modeling and computational framework…
A popular approach for addressing uncertainty in variational inequality problems is by solving the expected residual minimization (ERM) problem. This avenue necessitates distributional information associated with the uncertainty and…
We study a class of stochastic optimal design problems for elliptic partial differential equations in divergence form, where the coefficients represent mixtures of two conducting materials. The objective is to minimize a generalized risk…