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DoG is SGD's Best Friend: A Parameter-Free Dynamic Step Size Schedule

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arxiv 2302.12022 v3 pith:QYEPAZX5 submitted 2023-02-08 cs.LG math.OC

classification cs.LGmath.OC
keywords gradientslearningsteptuneddistancedynamicformulaparameter-free
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We propose a tuning-free dynamic SGD step size formula, which we call Distance over Gradients (DoG). The DoG step sizes depend on simple empirical quantities (distance from the initial point and norms of gradients) and have no ``learning rate'' parameter. Theoretically, we show that a slight variation of the DoG formula enjoys strong parameter-free convergence guarantees for stochastic convex optimization assuming only \emph{locally bounded} stochastic gradients. Empirically, we consider a broad range of vision and language transfer learning tasks, and show that DoG's performance is close to that of SGD with tuned learning rate. We also propose a per-layer variant of DoG that generally outperforms tuned SGD, approaching the performance of tuned Adam. A PyTorch implementation is available at https://github.com/formll/dog

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Cited by 2 Pith papers

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  1. Fantastic Pretraining Optimizers and Where to Find Them

    cs.LG 2025-09 conditional novelty 6.0 of 10

    After careful tuning, alternative optimizers speed up LLM pretraining by only 1.1x to 1.4x over AdamW, and the advantage shrinks with model scale.

  2. A Parameter-Free and Near-Optimal Zeroth-Order Algorithm for Stochastic Convex Optimization

    math.OC 2025-02 conditional novelty 5.0 of 10

    POEM is a parameter-free stochastic zeroth-order method that adapts both step size and smoothing automatically and reaches near-optimal oracle complexity.

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