A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems

Xu, Zi; Zhang, Huiling; Xu, Yang; Lan, Guanghui

doi:10.48550/arxiv.2006.02032

Cited by 14 publications

(19 citation statements)

References 25 publications

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“…Since there is an extensive literature on convergence rates in terms of a gap function or distance to a solution for monotone problems as well as generalizations such as nonconvex-concave [9,37], convex-nonconcave [58] or under the Polyak-Łojasiewicz assumption, see [59], we will only focus on the nonconvex-nonconcave setting and rates in terms of the gradient norm for the monotone setting.…”

Section: Related Literaturementioning

confidence: 99%

Solving Nonconvex-Nonconcave Min-Max Problems exhibiting Weak Minty Solutions

Böhm¹

2022

Preprint

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We investigate a structured class of nonconvex-nonconcave min-max problems exhibiting so-called weak Minty solutions, a notion which was only recently introduced, but is able to simultaneously capture different generalizations of monotonicity. We prove novel convergence results for a generalized version of the optimistic gradient method (OGDA) in this setting matching the ones recently shown for the extragradient method (EG). In addition we propose an adaptive stepsize version of EG, which does not require knowledge of the problem parameters.

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Section: Related Literaturementioning

confidence: 99%

Solving Nonconvex-Nonconcave Min-Max Problems exhibiting Weak Minty Solutions

Böhm¹

2022

Preprint

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“…We first convert the FedFair problem to a nonconvex-concave min-max problem. Then, we apply the alternating gradient projection (AGP) algorithm [4] to tackle the min-max problem without infringing the data privacy of any client. We also extend AGP to tackle the LCO problem in a similar privacy-preserving way.…”

Section: Solving the Fedfair And Lco Problemsmentioning

confidence: 99%

“…AGP [4] is designed to obtain a δ-stationary point of a nonconvex-concave minmax problem in O(δ −4 ) iterations. It alternatively updates primal and dual variables by employing simple projected gradient steps at each iteration.…”

Section: Solving the Fedfair And Lco Problemsmentioning

confidence: 99%

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FedFair: Training Fair Models In Cross-Silo Federated Learning

Chu,

Wang,

Dong

et al. 2021

Preprint

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Building fair machine learning models becomes more and more important. As many powerful models are built by collaboration among multiple parties, each holding some sensitive data, it is natural to explore the feasibility of training fair models in cross-silo federated learning so that fairness, privacy and collaboration can be fully respected simultaneously. However, it is a very challenging task, since it is far from trivial to accurately estimate the fairness of a model without knowing the private data of the participating parties. In this paper, we first propose a federated estimation method to accurately estimate the fairness of a model without infringing the data privacy of any party. Then, we use the fairness estimation to formulate a novel problem of training fair models in cross-silo federated learning. We develop FedFair, a well-designed federated learning framework, which can successfully train a fair model with high performance without any data privacy infringement. Our extensive experiments on three real-world data sets demonstrate the excellent fair model training performance of our method.

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“…The updates in ( 9) and ( 10) are performed in an alternating manner [35], implying that between every two communication rounds each data party updates its local variable once. In real-world VFL tasks, different data parties typically have imbalanced computational resources and complete their local updates within different time frames.…”

Section: B Asynchronous Min-max Optimization Algorithmmentioning

confidence: 99%

Achieving Model Fairness in Vertical Federated Learning

Shi¹,

Fan²,

Zhou³

et al. 2021

Preprint

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Vertical federated learning (VFL), which enables multiple enterprises possessing non-overlapped features to strengthen their machine learning models without disclosing their private data and model parameters, has received increasing attention lately. Similar to other machine learning algorithms, VFL suffers from fairness issues, i.e., the learned model may be unfairly discriminatory over the group with sensitive attributes. To tackle this problem, we propose a fair VFL framework in this work. First, we systematically formulate the problem of training fair models in VFL, where the learning task is modeled as a constrained optimization problem. To solve it in a federated manner, we consider its equivalent dual form and develop an asynchronous gradient coordinate-descent ascent algorithm, where each data party performs multiple parallelized local updates per communication round to effectively reduce the number of communication rounds. We prove that the algorithm finds a δ-stationary point of the dual objective in O(δ −4 ) communication rounds under mild conditions. Finally, extensive experiments on three benchmark datasets demonstrate the superior performance of our method in training fair models.

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A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems

Cited by 14 publications

References 25 publications

Solving Nonconvex-Nonconcave Min-Max Problems exhibiting Weak Minty Solutions

Solving Nonconvex-Nonconcave Min-Max Problems exhibiting Weak Minty Solutions

FedFair: Training Fair Models In Cross-Silo Federated Learning

Achieving Model Fairness in Vertical Federated Learning

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