تقرير
Convergence Properties of Stochastic Hypergradients
| العنوان: | Convergence Properties of Stochastic Hypergradients |
|---|---|
| المؤلفون: | Grazzi, Riccardo, Pontil, Massimiliano, Salzo, Saverio |
| المصدر: | Proceedings of The 24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021), PMLR 130:3826-3834 |
| سنة النشر: | 2020 |
| المجموعة: | Computer Science Statistics |
| مصطلحات موضوعية: | Statistics - Machine Learning, Computer Science - Machine Learning |
| الوصف: | Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of the gradient of the upper-level objective (hypergradient). In this work, we study stochastic approximation schemes for the hypergradient, which are important when the lower-level problem is empirical risk minimization on a large dataset. The method that we propose is a stochastic variant of the approximate implicit differentiation approach in (Pedregosa, 2016). We provide bounds for the mean square error of the hypergradient approximation, under the assumption that the lower-level problem is accessible only through a stochastic mapping which is a contraction in expectation. In particular, our main bound is agnostic to the choice of the two stochastic solvers employed by the procedure. We provide numerical experiments to support our theoretical analysis and to show the advantage of using stochastic hypergradients in practice. Comment: added experiments, a table of notation and some comments. 22 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2011.07122 |
| رقم الأكسشن: | edsarx.2011.07122 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |