Incremental Learning-to-Learn with Statistical Guarantees

Giulia Denevi, Carlo Ciliberto, Dimitris Stamos, Massimiliano Pontil
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:456-465, 2018.

Abstract

In learning-to-learn the goal is to infer a learning algorithm that works well on a class of tasks sampled from an unknown meta-distribution. In contrast to previous work on batch learning-to-learn, we consider a scenario where tasks are presented sequentially and the algorithm needs to adapt incrementally to improve its performance on future tasks. Key to this setting is for the algorithm to rapidly incorporate new observations into the model as they arrive, without keeping them in memory. We focus on the case where the underlying algorithm is Ridge Regression parametrised by a symmetric positive semidefinite matrix. We propose to learn this matrix by applying a stochastic strategy to minimize the empirical error incurred by Ridge Regression on future tasks sampled from the meta-distribution. We study the statistical properties of the proposed algorithm and prove non-asymptotic bounds on its excess transfer risk, that is, the generalization performance on new tasks from the same meta-distribution. We compare our online learning-to-learn approach with a state-of-the-art batch method, both theoretically and empirically.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-denevi18a, title = {Incremental Learning-to-Learn with Statistical Guarantees}, author = {Denevi, Giulia and Ciliberto, Carlo and Stamos, Dimitris and Pontil, Massimiliano}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {456--465}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/denevi18a/denevi18a.pdf}, url = {https://proceedings.mlr.press/r16/denevi18a.html}, abstract = {In learning-to-learn the goal is to infer a learning algorithm that works well on a class of tasks sampled from an unknown meta-distribution. In contrast to previous work on batch learning-to-learn, we consider a scenario where tasks are presented sequentially and the algorithm needs to adapt incrementally to improve its performance on future tasks. Key to this setting is for the algorithm to rapidly incorporate new observations into the model as they arrive, without keeping them in memory. We focus on the case where the underlying algorithm is Ridge Regression parametrised by a symmetric positive semidefinite matrix. We propose to learn this matrix by applying a stochastic strategy to minimize the empirical error incurred by Ridge Regression on future tasks sampled from the meta-distribution. We study the statistical properties of the proposed algorithm and prove non-asymptotic bounds on its excess transfer risk, that is, the generalization performance on new tasks from the same meta-distribution. We compare our online learning-to-learn approach with a state-of-the-art batch method, both theoretically and empirically.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Incremental Learning-to-Learn with Statistical Guarantees %A Giulia Denevi %A Carlo Ciliberto %A Dimitris Stamos %A Massimiliano Pontil %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-denevi18a %I PMLR %P 456--465 %U https://proceedings.mlr.press/r16/denevi18a.html %V R16 %X In learning-to-learn the goal is to infer a learning algorithm that works well on a class of tasks sampled from an unknown meta-distribution. In contrast to previous work on batch learning-to-learn, we consider a scenario where tasks are presented sequentially and the algorithm needs to adapt incrementally to improve its performance on future tasks. Key to this setting is for the algorithm to rapidly incorporate new observations into the model as they arrive, without keeping them in memory. We focus on the case where the underlying algorithm is Ridge Regression parametrised by a symmetric positive semidefinite matrix. We propose to learn this matrix by applying a stochastic strategy to minimize the empirical error incurred by Ridge Regression on future tasks sampled from the meta-distribution. We study the statistical properties of the proposed algorithm and prove non-asymptotic bounds on its excess transfer risk, that is, the generalization performance on new tasks from the same meta-distribution. We compare our online learning-to-learn approach with a state-of-the-art batch method, both theoretically and empirically. %Z Reissued by PMLR on 04 October 2026.
APA
Denevi, G., Ciliberto, C., Stamos, D. & Pontil, M.. (2018). Incremental Learning-to-Learn with Statistical Guarantees. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:456-465 Available from https://proceedings.mlr.press/r16/denevi18a.html. Reissued by PMLR on 04 October 2026.

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