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arXiv · 2105.04228

Exact asymptotic characterisation of running time for approximate gradient descent on random graphs

Matthieu Jonckheere·Manuel Sáenz
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Abstract

In this work we study the time complexity for the search of local minima in random graphs whose vertices have i.i.d. cost values. We show that, for Erd\"os-R\'enyi graphs with connection probability given by $\lambda/n^\alpha$ (with $\lambda > 0$ and $0 < \alpha < 1$), a family of local algorithms that approximate a gradient descent find local minima faster than the full gradient descent. Furthermore, we find a probabilistic representation for the running time of these algorithms leading to asymptotic estimates of the mean running times.

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Matthieu Jonckheere, Manuel Sáenz. 2021-05-10. Exact asymptotic characterisation of running time for approximate gradient descent on random graphs. https://arxiv.org/abs/2105.04228

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