Grazzi, Riccardo;
Pontil, Massimiliano;
Salzo, Saverio;
(2021)
Convergence Properties of Stochastic Hypergradients.
In: Banerjee, Arindam and Fukumizu, Kenji, (eds.)
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics.
(pp. pp. 3826-3834).
PMLR 130
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Abstract
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.
Type: | Proceedings paper |
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Title: | Convergence Properties of Stochastic Hypergradients |
Event: | 24th International Conference on Artificial Intelligence and Statistics |
Open access status: | An open access version is available from UCL Discovery |
Publisher version: | https://proceedings.mlr.press/v130/grazzi21a.html |
Language: | English |
Additional information: | This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions. |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
URI: | https://discovery.ucl.ac.uk/id/eprint/10164240 |
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