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

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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.

### Dates and versions

hal-03799715 , version 1 (06-10-2022)

### Identifiers

• HAL Id : hal-03799715 , version 1
• ARXIV :

### Cite

Matthieu Jonckheere, Manuel Sáenz. Exact asymptotic characterisation of running time for approximate gradient descent on random graphs. 2022. ⟨hal-03799715⟩

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