Related papers: Power Homotopy for Zeroth-Order Non-Convex Optimiz…
Hard optimization problems are often approached by finding approximate solutions. Here, we highlight the concept of proportional sampling and discuss how it can be used to improve the performance of stochastic algorithms for optimization.…
We introduce a new zeroth-order algorithm for private stochastic optimization on nonconvex and nonsmooth objectives. Given a dataset of size $M$, our algorithm ensures $(\alpha,\alpha\rho^2/2)$-R\'enyi differential privacy and finds a…
Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…
An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this…
We introduce Probabilistic Gaussian Homotopy (PGH), a probability-space continuation framework for nonconvex optimization. Unlike classical Gaussian homotopy, which smooths the objective and uniformly averages gradients, PGH deforms the…
This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$…
In recent years, random subspace methods have been actively studied for large-dimensional nonconvex problems. Recent subspace methods have improved theoretical guarantees such as iteration complexity and local convergence rate while…
We propose a globally convergent Gauss-Newton algorithm for finding a local optimal solution of a non-convex and possibly non-smooth optimization problem. The algorithm that we present is based on a Gauss-Newton-type iteration for the…
We propose a novel trust region method for solving a class of nonsmooth, nonconvex composite-type optimization problems. The approach embeds inexact semismooth Newton steps for finding zeros of a normal map-based stationarity measure for…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
This paper studies stochastic minimization of a finite-sum loss $ F (\mathbf{x}) = \frac{1}{N} \sum_{\xi=1}^N f(\mathbf{x};\xi) $. In many real-world scenarios, the Hessian matrix of such objectives exhibits a low-rank structure on a batch…
This paper shows how a class of non-convex optimization problems constrained by discretized nonlinear partial differential equations may be solved to global optimality using an interior point continuation method. The solution procedure…
Zero-shot hyperparameter optimization (HPO) is a simple yet effective use of transfer learning for constructing a small list of hyperparameter (HP) configurations that complement each other. That is to say, for any given dataset, at least…
The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…
Recent work on eigenvalues and eigenvectors for tensors of order m >= 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for…
This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging…
We consider a novel setting of zeroth order non-convex optimization, where in addition to querying the function value at a given point, we can also duel two points and get the point with the larger function value. We refer to this setting…
This paper studies first order methods for solving smooth minimax optimization problems $\min_x \max_y g(x,y)$ where $g(\cdot,\cdot)$ is smooth and $g(x,\cdot)$ is concave for each $x$. In terms of $g(\cdot,y)$, we consider two settings --…
Zeroth-order optimization addresses problems where gradient information is inaccessible or impractical to compute. While most existing methods rely on first-order approximations, incorporating second-order (curvature) information can, in…
Two-point zeroth order methods are important in many applications of zeroth-order optimization, such as robotics, wind farms, power systems, online optimization, and adversarial robustness to black-box attacks in deep neural networks, where…