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New research explores convergence in augmented primal-dual dynamics with sampled constraints

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This research paper investigates the stability and convergence of augmented primal-dual dynamics, particularly when constraint values are estimated from samples. The study identifies that unbiased constraint observations can lead to a biased augmented multiplier signal, which can shift the equilibria of the mean dynamics. To counteract this bias, the paper proposes a recursive estimation of constraint values before generating the augmented multiplier signal. For smooth convex conic problems, the authors establish boundedness of primal, dual, and estimation states, vanishing estimation error, and almost sure convergence to a KKT point under specific regularity conditions. AI

RANK_REASON The item is an academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=0.4]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New research explores convergence in augmented primal-dual dynamics with sampled constraints

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The item is an academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Kang Liu, Mengxiao Chen, Siqi Xiong, Yi Xia ·

    Equilibrium bias and convergence in augmented primal--dual dynamics with sampled constraints

    arXiv:2609.13925v1 Announce Type: cross Abstract: This work studies the stability and convergence of augmented primal-dual dynamics when constraint values are estimated from samples. Unbiased constraint observations can produce a biased augmented multiplier signal, shifting the e…

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