Computer Science > Machine Learning
arXiv:2207.08257 (cs)
[Submitted on 17 Jul 2022]
Title:Uniform Stability for First-Order Empirical Risk Minimization
View a PDF of the paper titled Uniform Stability for First-Order Empirical Risk Minimization, by Amit Attia and Tomer Koren
View PDFAbstract:We consider the problem of designing uniformly stable first-order optimization algorithms for empirical risk minimization. Uniform stability is often used to obtain generalization error bounds for optimization algorithms, and we are interested in a general approach to achieve it. For Euclidean geometry, we suggest a black-box conversion which given a smooth optimization algorithm, produces a uniformly stable version of the algorithm while maintaining its convergence rate up to logarithmic factors. Using this reduction we obtain a (nearly) optimal algorithm for smooth optimization with convergence rate $\widetilde{O}(1/T^2)$ and uniform stability $O(T^2/n)$, resolving an open problem of Chen et al. (2018); Attia and Koren (2021). For more general geometries, we develop a variant of Mirror Descent for smooth optimization with convergence rate $\widetilde{O}(1/T)$ and uniform stability $O(T/n)$, leaving open the question of devising a general conversion method as in the Euclidean case.
| Comments: | 18 pages, Proceedings of Thirty Fifth Conference on Learning Theory, PMLR 178:3313-3332, 2022 |
| Subjects: | Machine Learning (cs.LG); Optimization and Control (math.OC); Machine Learning (stat.ML) |
| Cite as: | arXiv:2207.08257 [cs.LG] |
| (orarXiv:2207.08257v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2207.08257 arXiv-issued DOI via DataCite |
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View a PDF of the paper titled Uniform Stability for First-Order Empirical Risk Minimization, by Amit Attia and Tomer Koren
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