Solving a Class of Non-Convex Min-Max Games Using Adaptive Momentum Methods

Barazandeh, Babak; Tarzanagh, Davoud Ataee; Michailidis, George

doi:10.1109/icassp39728.2021.9414476

Cited by 12 publications

(15 citation statements)

References 13 publications

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“…• Non-monotone case: In this setting the convergence is guaranteed up to some accuracy that is governed by the stochastic nature of the problem (the σ 2 term) and by the distributed nature of the problem (∆ terms). With this respect the results are similar to non-distributed stochastic extragradient method [3] and distributed method in the homogeneous case [37]. To the best of our knowledge, convergence up to arbitrarily small accuracy can be guaranteed only for deterministic distributed methods [38], i.e.…”

Section: Resultsmentioning

confidence: 67%

Decentralized Local Stochastic Extra-Gradient for Variational Inequalities

Beznosikov¹,

Dvurechensky²,

Koloskova³

et al. 2021

Preprint

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We consider decentralized stochastic variational inequalities where the problem data is distributed across many participating devices (heterogeneous, or non-IID data setting). We propose a novel method-based on stochastic extragradient-where participating devices can communicate over arbitrary, possibly time-varying network topologies. This covers both the fully decentralized optimization setting and the centralized topologies commonly used in Federated Learning. Our method further supports multiple local updates on the workers for reducing the communication frequency between workers. We theoretically analyze the proposed scheme in the strongly monotone, monotone and non-monotone setting. As a special case, our method and analysis apply in particular to decentralized stochastic min-max problems which are being studied with increased interest in Deep Learning. For example, the training objective of Generative Adversarial Networks (GANs) are typically saddle point problems and the decentralized training of GANs has been reported to be extremely challenging. While SOTA techniques rely on either repeated gossip rounds or proximal updates, we alleviate both of these requirements. Experimental results for decentralized GAN demonstrate the effectiveness of our proposed algorithm.

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Section: Resultsmentioning

confidence: 67%

Decentralized Local Stochastic Extra-Gradient for Variational Inequalities

Beznosikov¹,

Dvurechensky²,

Koloskova³

et al. 2021

Preprint

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show abstract

“…The focus of this paper is on the decentralized problem (Algorithm 2) and we only mention the most related corollary for Algorithm 1 in the sequel. Theoretical results and performance of Adam 3 on a single computing node are given in [85].…”

Section: A Decentralized Adaptive Momentum Algorithmmentioning

confidence: 99%

“…Corollary 4.1. (Rephrased from [85]) Algorithm 1 requires a total of O( −4 ) gradient evaluations of the objective function to find an -SFNE point of Game 1.…”

Section: A Decentralized Adaptive Momentum Algorithmmentioning

confidence: 99%

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A Decentralized Adaptive Momentum Method for Solving a Class of Min-Max Optimization Problems

Barazandeh,

Huang,

Michailidis

2021

Preprint

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Min-max saddle point games have recently been intensely studied, due to their wide range of applications, including training Generative Adversarial Networks (GANs). However, most of the recent efforts for solving them are limited to special regimes such as convex-concave games. Further, it is customarily assumed that the underlying optimization problem is solved either by a single machine or in the case of multiple machines connected in centralized fashion, wherein each one communicates with a central node. The latter approach becomes challenging, when the underlying communications network has low bandwidth. In addition, privacy considerations may dictate that certain nodes can communicate with a subset of other nodes. Hence, it is of interest to develop methods that solve min-max games in a decentralized manner. To that end, we develop a decentralized adaptive momentum (ADAM)-type algorithm for solving min-max optimization problem under the condition that the objective function satisfies a Minty Variational Inequality condition, which is a generalization to convex-concave case. The proposed method overcomes shortcomings of recent non-adaptive gradient-based decentralized algorithms for min-max optimization problems that do not perform well in practice and require careful tuning. In this paper, we obtain non-asymptotic rates of convergence of the proposed algorithm (coined Dadam 3 ) for finding a (stochastic) first-order Nash

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“…As such, existing positive results rely on adding this structure in one way or another. In particular, a common methodology is to "mimic" the case of a VI with a monotone operator [28] by imposing pseudomonotonicity, the Minty condition, or contraction of the best response mappings [67,68,69,70,71,72,73,74,75,76]. However, these assumptions are restrictive and rarely satisfied in modern applications; see [48] for a detailed discussion.…”

Section: Introductionmentioning

confidence: 99%

Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domain

Ostrovskii,

Barazandeh,

Razaviyayn

2021

Preprint

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We study the problem of finding approximate first-order stationary points in optimization problems of the form min x∈X max y∈Y f (x, y), where the sets X, Y are convex and Y is compact. The objective function f is smooth, but assumed neither convex in x nor concave in y. Our approach relies upon replacing the function f (x, ⋅) with its k-th order Taylor approximation (in y) and finding a near-stationary point in the resulting surrogate problem. To guarantee its success, we establish the following result: let the Euclidean diameter of Y be small in terms of the target accuracy ε, namely O(ε 2 k+1 ) for k ∈ N and O(ε) for k = 0, with the constant factors controlled by certain regularity parameters of f ; then any ε-stationary point in the surrogate problem remains O(ε)-stationary for the initial problem. Moreover, we show that these upper bounds are nearly optimal: the aforementioned reduction provably fails when the diameter of Y is larger. For 0 ⩽ k ⩽ 2 the surrogate function can be efficiently maximized in y; our general approximation result then leads to efficient algorithms for finding a near-stationary point in nonconvex-nonconcave min-max problems, for which we also provide convergence guarantees.

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Solving a Class of Non-Convex Min-Max Games Using Adaptive Momentum Methods

Cited by 12 publications

References 13 publications

Decentralized Local Stochastic Extra-Gradient for Variational Inequalities

Decentralized Local Stochastic Extra-Gradient for Variational Inequalities

A Decentralized Adaptive Momentum Method for Solving a Class of Min-Max Optimization Problems

Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domain

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