Related papers: Curvature-Aware Derivative-Free Optimization
Zeroth-order (ZO, also known as derivative-free) methods, which estimate the gradient only by two function evaluations, have attracted much attention recently because of its broad applications in machine learning community. The two function…
Decentralized optimization algorithms have attracted intensive interests recently, as it has a balanced communication pattern, especially when solving large-scale machine learning problems. Stochastic Path Integrated Differential Estimator…
The dual challenges of prohibitive communication overhead and the impracticality of gradient computation due to data privacy or black-box constraints in distributed systems motivate this work on communication-constrained gradient-free…
Zeroth-order (a.k.a, derivative-free) methods are a class of effective optimization methods for solving complex machine learning problems, where gradients of the objective functions are not available or computationally prohibitive.…
Consensus-based optimization (CBO) is an agent-based derivative-free method for non-smooth global optimization that has been introduced in 2017, leveraging a surprising interplay between stochastic exploration and Laplace principle. In…
Simplex-type methods, such as the well-known Nelder-Mead algorithm, are widely used in derivative-free optimization (DFO), particularly in practice. Despite their popularity, the theoretical understanding of their convergence properties has…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
We consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order queries. Under sparsity assumptions on the gradients or function values, we present two algorithms: a successive component/feature…
We propose STARS, a randomized derivative-free algorithm for unconstrained optimization when the function evaluations are contaminated with random noise. STARS takes dynamic, noise-adjusted smoothing step-sizes that minimize the…
Zeroth-order optimization aims to minimize an objective function using only function evaluations, and is therefore fundamental in black-box optimization, hyperparameter tuning, bandit learning, and adversarial machine learning. While…
In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We…
This paper explores the performance of a random Gaussian smoothing zeroth-order (ZO) scheme for minimising quasar-convex (QC) and strongly quasar-convex (SQC) functions in both unconstrained and constrained settings. For the unconstrained…
The conditional gradient algorithm (also known as the Frank-Wolfe algorithm) has recently regained popularity in the machine learning community due to its projection-free property to solve constrained problems. Although many variants of the…
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…
In this paper, we propose a new method based on the Sliding Algorithm from Lan(2016, 2019) for the convex composite optimization problem that includes two terms: smooth one and non-smooth one. Our method uses the stochastic noised…
In this work, we focus on the study of stochastic zeroth-order (ZO) optimization which does not require first-order gradient information and uses only function evaluations. The problem of ZO optimization has emerged in many recent machine…
Random search methods are widely used for global optimization due to their theoretical generality and implementation simplicity. This paper proposes a depth-first directional search (DFDS) algorithm for globally solving nonconvex…
We develop a new approximation theory for linear and quadratic interpolation models, suitable for use in convex-constrained derivative-free optimization (DFO). Most existing model-based DFO methods for constrained problems assume the…
Classical worst-case optimization theory neither explains the success of optimization in machine learning, nor does it help with step size selection. In this paper we demonstrate the viability and advantages of replacing the classical…
Two types of zeroth-order stochastic algorithms have recently been designed for nonconvex optimization respectively based on the first-order techniques SVRG and SARAH/SPIDER. This paper addresses several important issues that are still open…