Permutation-Based SGD: Is Random Optimal?
By Shashank Rajput, Kangwook Lee, Dimitris Papailiopoulos. 2021
16 citations recorded by the source corpus.
A recent line of ground-breaking results for permutation-based SGD has corroborated a widely observed phenomenon: random permutations offer faster convergence than with-replacement sampling. However, is random optimal? We show that this depends heavily on what functions we are optimizing, and the convergence gap between optimal and random permutations can vary from exponential to nonexistent. We first show that for 1-dimensional strongly convex functions, with smooth second derivatives, there exist optimal permutations that offer exponentially faster convergence compared to random. However, for general strongly convex functions, random permutations are optimal. Finally, we show that for quadratic, strongly-convex functions, there are easy-to-construct permutations that lead to accelerated convergence compared to random. Our results suggest that a general convergence characterization of optimal permutations cannot capture the nuances of individual function classes, and can mistakenly indicate that one cannot do much better than random.
Subfields: Optimization & Training
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In Optimization & Training
- Sebastian U. Stich
- Martin Jaggi
- Christopher De Sa
- Yucheng Lu
- Wentao Guo
- Peter Richtárik
- Hong Chang
- Amirkeivan Mohtashami
Citations in the corpus
- On The Impact of Machine Learning Randomness on Group Fairness (2023, background): “Data order during training governs gradient updates and thus its impact on fairness is unsurprising [32, 37, 42, 47, 48, 50].”
- GraB: Finding Provably Better Data Permutations than Random Reshuffling (2022, methodology): “Shuffle Once (SO) performs worst in all the cases, and FlipFlop is generally the same as RR, which is aligned with the conclusion made in Rajput et al. [4].”
- Characterizing & Finding Good Data Orderings for Fast Convergence of Sequential Gradient Methods (2022, background): “[22] shows that for 1-dimensional functions with smooth Hessian, a good order exists which yields exponential convergence, beating RR.”