Zeroth-Order Negative Curvature Finding: Escaping Saddle Points without Gradients

• URL: http://arxiv.org/abs/2210.01496v1
• Date: Tue, 4 Oct 2022 10:01:16 GMT
• Title: Zeroth-Order Negative Curvature Finding: Escaping Saddle Points without Gradients
• Authors: Hualin Zhang and Huan Xiong and Bin Gu
• Abstract summary: We consider escaping saddle points of non local problems where only the function evaluations can be accessed. We propose two zeroth-order negative curvature finding frameworks.
• Score: 22.153544816232042
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider escaping saddle points of nonconvex problems where only the function evaluations can be accessed. Although a variety of works have been proposed, the majority of them require either second or first-order information, and only a few of them have exploited zeroth-order methods, particularly the technique of negative curvature finding with zeroth-order methods which has been proven to be the most efficient method for escaping saddle points. To fill this gap, in this paper, we propose two zeroth-order negative curvature finding frameworks that can replace Hessian-vector product computations without increasing the iteration complexity. We apply the proposed frameworks to ZO-GD, ZO-SGD, ZO-SCSG, ZO-SPIDER and prove that these ZO algorithms can converge to $(\epsilon,\delta)$-approximate second-order stationary points with less query complexity compared with prior zeroth-order works for finding local minima.

Related papers

• Obtaining Lower Query Complexities through Lightweight Zeroth-Order Proximal Gradient Algorithms [65.42376001308064]
  We propose two variance reduced ZO estimators for complex gradient problems. We improve the state-of-the-art function complexities from $mathcalOleft(minfracdn1/2epsilon2, fracdepsilon3right)$ to $tildecalOleft(fracdepsilon2right)$.
  arXiv  Detail & Related papers  (2024-10-03T15:04:01Z)
• Explicit Second-Order Min-Max Optimization Methods with Optimal Convergence Guarantee [86.05440220344755]
  We propose and analyze inexact regularized Newton-type methods for finding a global saddle point of emphcon unconstrained min-max optimization problems. We show that the proposed methods generate iterates that remain within a bounded set and that the iterations converge to an $epsilon$-saddle point within $O(epsilon-2/3)$ in terms of a restricted function.
  arXiv  Detail & Related papers  (2022-10-23T21:24:37Z)
• Derivative-free Alternating Projection Algorithms for General Nonconvex-Concave Minimax Problems [9.173866646584031]
  In this paper, we propose an algorithm for nonsmooth zeroth-order minimax problems. We show that it can be used to attack nonconcave minimax problems.
  arXiv  Detail & Related papers  (2021-08-01T15:23:49Z)
• Zeroth-Order Algorithms for Smooth Saddle-Point Problems [117.44028458220427]
  We propose several algorithms to solve saddle-point problems using zeroth-order oracles. Our analysis shows that our convergence rate for the term is only by a $log n$ factor worse than for the first-order methods. We also consider a mixed setup and develop 1/2th-order methods that use zeroth-order oracle for the part.
  arXiv  Detail & Related papers  (2020-09-21T14:26:48Z)
• Second-Order Information in Non-Convex Stochastic Optimization: Power and Limitations [54.42518331209581]
  We find an algorithm which finds. epsilon$-approximate stationary point (with $|nabla F(x)|le epsilon$) using. $(epsilon,gamma)$surimate random random points. Our lower bounds here are novel even in the noiseless case.
  arXiv  Detail & Related papers  (2020-06-24T04:41:43Z)
• Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandits [99.70167985955352]
  We study the problem of zero-order optimization of a strongly convex function. We consider a randomized approximation of the projected gradient descent algorithm. Our results imply that the zero-order algorithm is nearly optimal in terms of sample complexity and the problem parameters.
  arXiv  Detail & Related papers  (2020-06-14T10:42:23Z)
• Nonconvex Zeroth-Order Stochastic ADMM Methods with Lower Function Query Complexity [109.54166127479093]
  Zeroth-order (a.k.a, derivative-free) methods are a class of effective optimization methods for solving machine learning problems. In this paper, we propose a class faster faster zerothorder alternating gradient method multipliers (MMADMM) to solve the non finitesum problems. We show that ZOMMAD methods can achieve a lower function $O(frac13nfrac1)$ for finding an $epsilon$-stationary point. At the same time, we propose a class faster zerothorder online ADM methods (M
  arXiv  Detail & Related papers  (2019-07-30T02:21:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.