Related papers: A Stochastic Quasi-Newton Method for Non-convex Op…

Stochastic composition optimization draws much attention recently and has been successful in many emerging applications of machine learning, statistical analysis, and reinforcement learning. In this paper, we focus on the composition…

We propose an adaptive smoothing algorithm based on Nesterov's smoothing technique in \cite{Nesterov2005c} for solving "fully" nonsmooth composite convex optimization problems. Our method combines both Nesterov's accelerated proximal…

The incremental gradient method is a prominent algorithm for minimizing a finite sum of smooth convex functions, used in many contexts including large-scale data processing applications and distributed optimization over networks. It is a…

In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…

In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…

We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…

This paper studies quasi-Newton methods for solving strongly-convex-strongly-concave saddle point problems (SPP). We propose greedy and random Broyden family updates for SPP, which have explicit local superlinear convergence rate of…

We focus on nonconvex and nonsmooth minimization problems with a composite objective, where the differentiable part of the objective is freed from the usual and restrictive global Lipschitz gradient continuity assumption. This longstanding…

Smoothness is known to be crucial for acceleration in offline optimization, and for gradient-variation regret minimization in online learning. Interestingly, these two problems are actually closely connected -- accelerated optimization can…

We provide a lower bound showing that the $O(1/k)$ convergence rate of the NoLips method (a.k.a. Bregman Gradient) is optimal for the class of functions satisfying the $h$-smoothness assumption. This assumption, also known as relative…

Gradient normalization and soft clipping are two popular techniques for tackling instability issues and improving convergence of stochastic gradient descent (SGD) with momentum. In this article, we study these types of methods through the…

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…

We study first-order methods for convex optimization problems with functions $f$ satisfying the recently proposed $\ell$-smoothness condition $||\nabla^{2}f(x)|| \le \ell\left(||\nabla f(x)||\right),$ which generalizes the $L$-smoothness…

Non-convex Machine Learning problems typically do not adhere to the standard smoothness assumption. Based on empirical findings, Zhang et al. (2020b) proposed a more realistic generalized $(L_0, L_1)$-smoothness assumption, though it…

This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…

Gradient clipping is a commonly used technique to stabilize the training process of neural networks. A growing body of studies has shown that gradient clipping is a promising technique for dealing with the heavy-tailed behavior that emerged…

This work proposes an accelerated first-order algorithm we call the Robust Momentum Method for optimizing smooth strongly convex functions. The algorithm has a single scalar parameter that can be tuned to trade off robustness to gradient…

In this paper, we propose the first Quasi-Newton method with a global convergence rate of $O(k^{-1})$ for general convex functions. Quasi-Newton methods, such as BFGS, SR-1, are well-known for their impressive practical performance.…