On Convergence of Incremental Gradient for Non-convex Smooth Functions

Anastasia Koloskova, Nikita Doikov, Sebastian U Stich, Martin Jaggi
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:25058-25086, 2024.

Abstract

In machine learning and neural network optimization, algorithms like incremental gradient, single shuffle SGD, and random reshuffle SGD are popular due to their cache-mismatch efficiency and good practical convergence behavior. However, their optimization properties in theory, especially for non-convex smooth functions, remain incompletely explored. This paper delves into the convergence properties of SGD algorithms with arbitrary data ordering, within a broad framework for non-convex smooth functions. Our findings show enhanced convergence guarantees for incremental gradient and single shuffle SGD. Particularly if $n$ is the training set size, we improve $n$ times the optimization term of convergence guarantee to reach accuracy $\epsilon$ from $O \left( \frac{n}{\epsilon} \right)$ to $O \left( \frac{1}{\epsilon}\right)$.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-koloskova24a, title = {On Convergence of Incremental Gradient for Non-convex Smooth Functions}, author = {Koloskova, Anastasia and Doikov, Nikita and Stich, Sebastian U and Jaggi, Martin}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {25058--25086}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/koloskova24a/koloskova24a.pdf}, url = {https://proceedings.mlr.press/v235/koloskova24a.html}, abstract = {In machine learning and neural network optimization, algorithms like incremental gradient, single shuffle SGD, and random reshuffle SGD are popular due to their cache-mismatch efficiency and good practical convergence behavior. However, their optimization properties in theory, especially for non-convex smooth functions, remain incompletely explored. This paper delves into the convergence properties of SGD algorithms with arbitrary data ordering, within a broad framework for non-convex smooth functions. Our findings show enhanced convergence guarantees for incremental gradient and single shuffle SGD. Particularly if $n$ is the training set size, we improve $n$ times the optimization term of convergence guarantee to reach accuracy $\epsilon$ from $O \left( \frac{n}{\epsilon} \right)$ to $O \left( \frac{1}{\epsilon}\right)$.} }
Endnote
%0 Conference Paper %T On Convergence of Incremental Gradient for Non-convex Smooth Functions %A Anastasia Koloskova %A Nikita Doikov %A Sebastian U Stich %A Martin Jaggi %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-koloskova24a %I PMLR %P 25058--25086 %U https://proceedings.mlr.press/v235/koloskova24a.html %V 235 %X In machine learning and neural network optimization, algorithms like incremental gradient, single shuffle SGD, and random reshuffle SGD are popular due to their cache-mismatch efficiency and good practical convergence behavior. However, their optimization properties in theory, especially for non-convex smooth functions, remain incompletely explored. This paper delves into the convergence properties of SGD algorithms with arbitrary data ordering, within a broad framework for non-convex smooth functions. Our findings show enhanced convergence guarantees for incremental gradient and single shuffle SGD. Particularly if $n$ is the training set size, we improve $n$ times the optimization term of convergence guarantee to reach accuracy $\epsilon$ from $O \left( \frac{n}{\epsilon} \right)$ to $O \left( \frac{1}{\epsilon}\right)$.
APA
Koloskova, A., Doikov, N., Stich, S.U. & Jaggi, M.. (2024). On Convergence of Incremental Gradient for Non-convex Smooth Functions. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:25058-25086 Available from https://proceedings.mlr.press/v235/koloskova24a.html.

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