相关论文: Adaptive Sampling-Based Bi-Fidelity Stochastic Tru…

This paper presents an adaptive hyperviscosity stabilisation procedure for the Radial Basis Function-generated Finite Difference (RBF-FD) method, aimed at solving linear and non-linear advection-dominated transport equations on domains…

The federated learning (FL) framework trains a machine learning model using decentralized data stored at edge client devices by periodically aggregating locally trained models. Popular optimization algorithms of FL use vanilla (stochastic)…

Federated learning (FL) algorithms usually sample a fraction of clients in each round (partial participation) when the number of participants is large and the server's communication bandwidth is limited. Recent works on the convergence…

In model-free reinforcement learning, the temporal difference method and its variants become unstable when combined with nonlinear function approximations. Bellman residual minimization with stochastic gradient descent (SGD) is more stable,…

Random Feature Models (RFMs) have become a powerful tool for approximating multivariate functions and solving partial differential equations efficiently. Sparse Random Feature Expansions (SRFE) improve traditional RFMs by incorporating…

We consider a federated learning (FL) system consisting of multiple clients and a server, where the clients aim to collaboratively learn a common decision model from their distributed data. Unlike the conventional FL framework that assumes…

We study a hierarchical federated learning (FL) problem, where clients cooperatively seek to select among multiple optimal solutions of a primary distributed learning problem, a solution that minimizes a secondary loss function. This…

In this work, we utilize a Trust Region based Derivative Free Optimization (DFO-TR) method to directly maximize the Area Under Receiver Operating Characteristic Curve (AUC), which is a nonsmooth, noisy function. We show that AUC is a smooth…

Stochastic variational inference allows for fast posterior inference in complex Bayesian models. However, the algorithm is prone to local optima which can make the quality of the posterior approximation sensitive to the choice of…

This thesis presents recent advances in model order reduction methods with the primary aim to construct online-efficient reduced surrogate models for parameterized multiscale phenomena and accelerate large-scale PDE-constrained parameter…

Self-Taught Reasoners (STaR), synonymously known as Rejection sampling Fine-Tuning (RFT), is an integral part of the training pipeline of self-improving reasoning Language Models (LMs). The self-improving mechanism often employs random…

In this work, we propose a novel adaptive stochastic gradient-free (ASGF) approach for solving high-dimensional nonconvex optimization problems based on function evaluations. We employ a directional Gaussian smoothing of the target function…

We present a trust-region-based adaptive finite-element algorithm for numerically solving a class of nonsmooth PDE-constrained optimization problems that includes problems with sparsifying regularizers and convex constraints. In particular,…

Bayesian optimization (BO) is increasingly employed in critical applications to find the optimal design with minimal cost. While BO is known for its sample efficiency, relying solely on costly high-fidelity data can still result in high…

Numerous applications in biology, statistics, science, and engineering require generating samples from high-dimensional probability distributions. In recent years, the Hamiltonian Monte Carlo (HMC) method has emerged as a state-of-the-art…

In many applications of mathematical optimization, one may wish to optimize an objective function without access to its derivatives. These situations call for derivative-free optimization (DFO) methods. Among the most successful approaches…

We propose a novel sampling-based federated learning framework for statistical inference on M-estimators with non-smooth objective functions, which frequently arise in modern statistical applications such as quantile regression and AUC…

This article presents a randomized matrix-free method for approximating the trace of $f({\bf A})$, where ${\bf A}$ is a large symmetric matrix and $f$ is a function analytic in a closed interval containing the eigenvalues of ${\bf A}$. Our…

Derivative-Free optimization (DFO) focuses on designing methods to solve optimization problems without the analytical knowledge of gradients of the objective function. There are two main families of DFO methods: model-based methods and…

Submodular functions have applications throughout machine learning, but in many settings, we do not have direct access to the underlying function $f$. We focus on stochastic functions that are given as an expectation of functions over a…