Related papers: Lower Bounds for Non-Convex Stochastic Optimizatio…
We study the secure stochastic convex optimization problem. A learner aims to learn the optimal point of a convex function through sequentially querying a (stochastic) gradient oracle. In the meantime, there exists an adversary who aims to…
This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…
A popular approach to minimize a finite-sum of convex functions is stochastic gradient descent (SGD) and its variants. Fundamental research questions associated with SGD include: (i) To find a lower bound on the number of times that the…
We analyze stochastic gradient algorithms for optimizing nonconvex problems. In particular, our goal is to find local minima (second-order stationary points) instead of just finding first-order stationary points which may be some bad…
We study the problem of zero-order optimization of a strongly convex function. The goal is to find the minimizer of the function by a sequential exploration of its values, under measurement noise. We study the impact of higher order…
This paper is devoted to the analysis of worst case complexity bounds for linesearch-type derivative-free algorithms for the minimization of general non-convex smooth functions. We prove that two linesearch-type algorithms enjoy the same…
Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are…
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…
During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…
Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we show for any Lipschitz, weakly convex objectives and…
We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first…
The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in…
We propose perturbed proximal algorithms that can provably escape strict saddles for nonsmooth weakly convex functions. The main results are based on a novel characterization of $\epsilon$-approximate local minimum for nonsmooth functions,…
Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…
This paper studies the complexity for finding approximate stationary points of nonconvex-strongly-concave (NC-SC) smooth minimax problems, in both general and averaged smooth finite-sum settings. We establish nontrivial lower complexity…
A parametric class of trust-region algorithms for constrained nonconvex optimization is analyzed, where the objective function is never computed. By defining appropriate first-order stationarity criteria, we are able to extend the Adagrad…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
We propose a family of nonconvex optimization algorithms that are able to save gradient and negative curvature computations to a large extent, and are guaranteed to find an approximate local minimum with improved runtime complexity. At the…
In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting and saddle-point avoiding. To handle…