Authors: Huiling Zhang, Zi Xu, Yuhong Dai

Published on: January 26, 2024

Impact Score: 8.54

Arxiv code: Arxiv:2402.03352

Summary

• What is new: The first two zeroth-order algorithms with iterative complexity guarantees for solving nonconvex-(strongly) concave minimax problems with coupled linear constraints under deterministic and stochastic settings.
• Why this is important: Addressing nonconvex minimax problems with coupled linear constraints in areas like machine learning and signal processing, which are challenging due to their complexity.
• What the research proposes: Introducing two single-loop algorithms, ZO-PDAPG and ZO-RMPDPG, for deterministic and stochastic settings of these problems, enhancing efficiency and solution precision.
• Results: Achieved iteration complexity of $\mathcal{O}(\varepsilon ^{-2})$ (deterministic nonconvex-strongly concave) and $\tilde{\mathcal{O}}(\varepsilon ^{-3})$ (stochastic), showing significant improvements in solving these problems efficiently.

Technical Details

Technological frameworks used: nan

Models used: Zero-order primal-dual alternating projected gradient (ZO-PDAPG), Zero-order regularized momentum primal-dual projected gradient (ZO-RMPDPG)

Data used: nan

Potential Impact

Machine learning, signal processing industries, and any sector involved in adversarial attacks in resource allocation and network flow problems.

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