Stochastic Recursive Gradient Descent Ascent for Stochastic Nonconvex-Strongly-Concave Minimax Problems

• URL: http://arxiv.org/abs/2001.03724v2
• Date: Fri, 23 Oct 2020 09:37:38 GMT
• Title: Stochastic Recursive Gradient Descent Ascent for Stochastic Nonconvex-Strongly-Concave Minimax Problems
• Authors: Luo Luo, Haishan Ye, Zhichao Huang, Tong Zhang
• Abstract summary: In this paper, we propose a novel method called RecurEnti Ascent (SREDA), which estimates more efficiently using variance. This method achieves the best known for this problem.
• Score: 36.645753881826955
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: We consider nonconvex-concave minimax optimization problems of the form $\min_{\bf x}\max_{\bf y\in{\mathcal Y}} f({\bf x},{\bf y})$, where $f$ is strongly-concave in $\bf y$ but possibly nonconvex in $\bf x$ and ${\mathcal Y}$ is a convex and compact set. We focus on the stochastic setting, where we can only access an unbiased stochastic gradient estimate of $f$ at each iteration. This formulation includes many machine learning applications as special cases such as robust optimization and adversary training. We are interested in finding an ${\mathcal O}(\varepsilon)$-stationary point of the function $\Phi(\cdot)=\max_{\bf y\in{\mathcal Y}} f(\cdot, {\bf y})$. The most popular algorithm to solve this problem is stochastic gradient decent ascent, which requires $\mathcal O(\kappa^3\varepsilon^{-4})$ stochastic gradient evaluations, where $\kappa$ is the condition number. In this paper, we propose a novel method called Stochastic Recursive gradiEnt Descent Ascent (SREDA), which estimates gradients more efficiently using variance reduction. This method achieves the best known stochastic gradient complexity of ${\mathcal O}(\kappa^3\varepsilon^{-3})$, and its dependency on $\varepsilon$ is optimal for this problem.

Related papers

• Projection-Free Methods for Stochastic Simple Bilevel Optimization with Convex Lower-level Problem [16.9187409976238]
  We study a class of convex bilevel optimization problems, also known as simple bilevel optimization. We introduce novel bilevel optimization methods that approximate the solution set of the lower-level problem.
  arXiv  Detail & Related papers  (2023-08-15T02:37:11Z)
• Faster Gradient-Free Algorithms for Nonsmooth Nonconvex Stochastic Optimization [20.54801745090522]
  We consider the problem of the form $min_x in mathbbRd f(x) triangleq mathbbE_xi [Fxi]$inf(x)$ Lipschitz. The recently proposed gradient-free method requires at most $mathcalO( L4 d3/2 epsilon-4 + Goldstein L d3/2 delta-1 epsilon-4)$ zeroth-order complexity
  arXiv  Detail & Related papers  (2023-01-16T13:33:37Z)
• ReSQueing Parallel and Private Stochastic Convex Optimization [59.53297063174519]
  We introduce a new tool for BFG convex optimization (SCO): a Reweighted Query (ReSQue) estimator for the gradient of a function convolved with a (Gaussian) probability density. We develop algorithms achieving state-of-the-art complexities for SCO in parallel and private settings.
  arXiv  Detail & Related papers  (2023-01-01T18:51:29Z)
• An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization [25.00475462213752]
  Decentralized Recursive desc. Method (DREAM) Concretely, it requires $mathcalO(minminappaappa3eps-3,kappa2 N)$ first-order oracle (SFO) calls and $tildemathcalO(kappa2 epsilon-2) communication rounds. Our numerical experiments validate the superiority of previous methods.
  arXiv  Detail & Related papers  (2022-12-05T16:09:39Z)
• Optimal Gradient Sliding and its Application to Distributed Optimization Under Similarity [121.83085611327654]
  We structured convex optimization problems with additive objective $r:=p + q$, where $r$ is $mu$-strong convex similarity. We proposed a method to solve problems master to agents' communication and local calls. The proposed method is much sharper than the $mathcalO(sqrtL_q/mu)$ method.
  arXiv  Detail & Related papers  (2022-05-30T14:28:02Z)
• Decentralized Stochastic Variance Reduced Extragradient Method [25.21457349137344]
  This paper studies decentralized convex-concave minimax optimization problems of the form $min_xmax_y fx,y triqfrac1msumi=1m f_i triqfrac1msumi=1m f_i triqfrac1msumi=1m f_i triqfrac1msumi=1m f_i triqfrac1msum
  arXiv  Detail & Related papers  (2022-02-01T16:06:20Z)
• Faster Perturbed Stochastic Gradient Methods for Finding Local Minima [92.99933928528797]
  We propose tttPullback, a faster perturbed gradient framework for finding local minima. We show that Pullback with gradient estimators such as SARAH/SP and STORM can find $(epsilon, epsilon_H)$approximate local minima within $tilde O(epsilon-3 + H-6)$. The core idea of our framework is a step-size pullback'' scheme to control the average movement of the gradient evaluations.
  arXiv  Detail & Related papers  (2021-10-25T07:20:05Z)
• Greedy Adversarial Equilibrium: An Efficient Alternative to Nonconvex-Nonconcave Min-Max Optimization [28.431572772564518]
  We show that Lipschitzitz's $varepsilon$-greedy adversarial model converges from any starting point to a $max_z f(x, z)$. We also show that Lipschitz's $nabla_y f(x,y)$ is in the dimension $d$, $1/varepsilon$, and the bounds on $nabla2_y f(x,y)$ are $nabla2_y.
  arXiv  Detail & Related papers  (2020-06-22T16:03:41Z)
• Agnostic Learning of a Single Neuron with Gradient Descent [92.7662890047311]
  We consider the problem of learning the best-fitting single neuron as measured by the expected square loss. For the ReLU activation, our population risk guarantee is $O(mathsfOPT1/2)+epsilon$. For the ReLU activation, our population risk guarantee is $O(mathsfOPT1/2)+epsilon$.
  arXiv  Detail & Related papers  (2020-05-29T07:20:35Z)
• Near-Optimal Algorithms for Minimax Optimization [115.21519161773287]
  The paper presents the first with $tildeO(sqrtkappa_mathbf xkappa_mathbf)$, matching the design on logarithmic factors. The paper also presents algorithms that match or outperform all existing methods in these settings in terms of complexity.
  arXiv  Detail & Related papers  (2020-02-05T16:49:09Z)
• On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems [86.92205445270427]
  We consider non-con minimax problems, $min_mathbfx max_mathhidoty f(mathbfdoty)$ efficiently.
  arXiv  Detail & Related papers  (2019-06-02T03:03:45Z)

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.