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arXiv · 2504.01898

Analysis of an Idealized Stochastic Polyak Method and its Application to Black-Box Model Distillation

Robert M. Gower·Guillaume Garrigos·Nicolas Loizou·Dimitris Oikonomou·Konstantin Mishchenko·Fabian Schaipp
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Abstract

We provide a general convergence theorem of an idealized stochastic Polyak step size called SPS$^*$. Besides convexity, we only assume a local expected gradient bound, that includes locally smooth and locally Lipschitz losses as special cases. We refer to SPS$^*$ as idealized because it requires access to the loss for every training batch evaluated at a solution. It is also ideal, in that it achieves the optimal lower bound for globally Lipschitz function, and is the first Polyak step size to have an $O(1/\sqrt{t})$ anytime convergence in the smooth setting. We show how to combine SPS$^*$ with momentum to achieve the same favorable rates for the last iterate. We conclude with several experiments to validate our theory, and a more practical setting showing how we can distill a teacher GPT-2 model into a smaller student model without any hyperparameter tuning.

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Robert M. Gower, Guillaume Garrigos, Nicolas Loizou, Dimitris Oikonomou, Konstantin Mishchenko, Fabian Schaipp. 2025-04-02. Analysis of an Idealized Stochastic Polyak Method and its Application to Black-Box Model Distillation. https://arxiv.org/abs/2504.01898

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