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Integration Methods and Accelerated Optimization Algorithms

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arxiv 1702.06751 v1 pith:CVSYVV4S submitted 2017-02-22 math.OC

Integration Methods and Accelerated Optimization Algorithms

classification math.OC
keywords equationintegrationaccelerateddifferentialflowgradientmethodsmulti-step
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We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the differential equation considered here is the basic gradient flow and we show that multi-step schemes allow integration of this differential equation using larger step sizes, thus intuitively explaining acceleration results.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Adaptive Federated Optimization

    cs.LG 2020-02 unverdicted novelty 6.0

    Proposes federated adaptive optimizers (FedAdagrad, FedAdam, FedYogi) with convergence analysis for non-convex objectives under data heterogeneity and reports empirical gains over FedAvg.

  2. Restart and Adaptive Acceleration in Stochastic Gradient Methods

    math.OC 2026-06 conditional novelty 5.0

    Restart schemes for SGD on KL-satisfying non-smooth weakly convex problems deliver accelerated convergence robust to exponent misspecification, with optimal schedules resembling Polyak steps.