Related papers: Hessian Initialization Strategies for L-BFGS Solvi…
Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding…
The Finite Fourier Series (FFS) Shape-Based (SB) trajectory approximation method has been used to rapidly generate initial trajectories that satisfy the dynamics, trajectory boundary conditions, and limitation on maximum thrust…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
We introduce Flat Hilbert Bayesian Inference (FHBI), an algorithm designed to enhance generalization in Bayesian inference. Our approach involves an iterative two-step procedure with an adversarial functional perturbation step and a…
3D Gaussian Splatting reconstructs scenes by starting from a sparse Structure-from-Motion initialization and refining under-reconstructed regions. This process is slow, as it requires multiple densification steps where Gaussians are…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…
In this paper, we study the generalized phase retrieval problem: to recover a signal $\bm{x}\in\mathbb{C}^n$ from the measurements $y_r=\lvert \langle\bm{a}_r,\bm{x}\rangle\rvert^2$, $r=1,2,\ldots,m$. The problem can be reformulated as a…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
We consider the development of practical stochastic quasi-Newton, and in particular Kronecker-factored block-diagonal BFGS and L-BFGS methods, for training deep neural networks (DNNs). In DNN training, the number of variables and components…
We develop a Levenberg-Marquardt method for minimizing the sum of a smooth nonlinear least-squar es term $f(x) = \tfrac{1}{2} \|F(x)\|_2^2$ and a nonsmooth term $h$. Both $f$ and $h$ may be nonconvex. Steps are computed by minimizing the…
Recent advances in 3D Gaussian Splatting (3DGS) have focused on accelerating optimization while preserving reconstruction quality. However, many proposed methods entangle implementation-level improvements with fundamental algorithmic…
This paper focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of $f$…
We analyze Newton's method with lazy Hessian updates for solving general possibly non-convex optimization problems. We propose to reuse a previously seen Hessian for several iterations while computing new gradients at each step of the…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on…
Over the past decade, stochastic algorithms have emerged as scalable and efficient tools for solving large-scale ill-posed inverse problems by randomly selecting subsets of equations at each iteration. However, due to the ill-posedness and…
Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…
Iteratively reweighted least square (IRLS) is a popular approach to solve sparsity-enforcing regression problems in machine learning. State of the art approaches are more efficient but typically rely on specific coordinate pruning schemes.…
The training of over-parameterized neural networks has received much study in recent literature. An important consideration is the regularization of over-parameterized networks due to their highly nonconvex and nonlinear geometry. In this…