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New variance-reduced methods accelerate root-finding algorithms

By PulseAugur Editorial · [1 sources] ·

Researchers have developed new variance-reduced fast Krasnoselkii-Mann methods to efficiently solve finite-sum root-finding problems. These methods achieve improved convergence rates, specifically O(1/k^2) and o(1/k^2) for the last-iterate convergence in terms of expected squared norm of the gradient. The framework is instantiated with SVRG and SAGA estimators, offering an oracle complexity of O(n + n^(2/3)ε^(-1)) to reach an ε-solution. The approach is also extended to handle finite-sum inclusions, maintaining theoretical guarantees, and has demonstrated promising performance in numerical experiments. AI

RANK_REASON The cluster contains an academic paper detailing new mathematical methods and their theoretical guarantees. [lever_c_demoted from research: ic=1 ai=0.4]

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New variance-reduced methods accelerate root-finding algorithms

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The cluster contains an academic paper detailing new mathematical methods and their theoretical guarantees. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Quoc Tran-Dinh ·

    Variance-Reduced Fast Krasnoselkii-Mann Methods for Finite-Sum Root-Finding Problems

    arXiv:2406.02413v4 Announce Type: replace-cross Abstract: We propose a new class of fast Krasnoselkii--Mann methods with variance reduction to solve a finite-sum co-coercive equation $Gx = 0$. Our algorithm is single-loop and leverages a new family of unbiased variance-reduced es…

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