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Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networks

28 May 2021arXiv:2105.13937archive 2025-07-28

Dong-Young Lim, Sotirios Sabanis

We present a new class of Langevin based algorithms, which overcomes many of the known shortcomings of popular adaptive optimizers that are currently used for the fine tuning of deep learning models. Its underpinning theory relies on recent advances of Euler's polygonal approximations for stochastic differential equations (SDEs) with monotone coefficients. As a result, it inherits the stability properties of tamed algorithms, while it addresses other known issues, e.g. vanishing gradients in neural networks. In particular, we provide a nonasymptotic analysis and full theoretical guarantees for the convergence properties of an algorithm of this novel class, which we named THεO POULA (or, simply, TheoPouLa). Finally, several experiments are presented with different types of deep learning models, which show the superior performance of TheoPouLa over many popular adaptive optimization algorithms.

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