Related papers: Stochastic Composition Optimization of Functions w…

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…

The stochastic composition optimization proposed recently by Wang et al. [2014] minimizes the objective with the compositional expectation form: $\min_x~(\mathbb{E}_iF_i \circ \mathbb{E}_j G_j)(x).$ It summarizes many important applications…

A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…

We consider the case of derivative-free algorithms for non-convex optimization, also known as zero order algorithms, that use only function evaluations rather than gradients. For a wide variety of gradient approximators based on finite…

Optimization problems with access to only zeroth-order information of the objective function on Riemannian manifolds arise in various applications, spanning from statistical learning to robot learning. While various zeroth-order algorithms…

We consider the problem of minimizing a $d$-dimensional Lipschitz convex function using a stochastic gradient oracle. We introduce and motivate a setting where the noise of the stochastic gradient is isotropic in that it is bounded in every…

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

In many important machine learning applications, the standard assumption of having a globally Lipschitz continuous gradient may fail to hold. This paper delves into a more general $(L_0, L_1)$-smoothness setting, which gains particular…

For the composite multi-objective optimization problem composed of two nonsmooth terms, a smoothing method is used to overcome the nonsmoothness of the objective function, making the objective function contain at most one nonsmooth term.…

In this paper, we propose a class of penalty methods with stochastic approximation for solving stochastic nonlinear programming problems. We assume that only noisy gradients or function values of the objective function are available via…

We consider (stochastic) subgradient methods for strongly convex but potentially nonsmooth non-Lipschitz optimization. We provide new equivalent dual descriptions (in the style of dual averaging) for the classic subgradient method, the…

We prove the first convergence guarantees for a subgradient method minimizing a generic Lipschitz function over generic Lipschitz inequality constraints. No smoothness or convexity (or weak convexity) assumptions are made. Instead, we…

In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the…

This paper considers optimization of smooth nonconvex functionals in smooth infinite dimensional spaces. A H\"older gradient descent algorithm is first proposed for finding approximate first-order points of regularized polynomial…

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…

In this work, we describe a generic approach to show convergence with high probability for both stochastic convex and non-convex optimization with sub-Gaussian noise. In previous works for convex optimization, either the convergence is only…

This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the…

We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…

This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are…

Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…