Timezone: »
The problem of learning-to-learn (LTL) or meta-learning is gaining increasing attention due to recent empirical evidence of its effectiveness in applications. The goal addressed in LTL is to select an algorithm that works well on tasks sampled from a meta-distribution. In this work, we consider the family of algorithms given by a variant of Ridge Regression, in which the regularizer is the square distance to an unknown mean vector. We show that, in this setting, the LTL problem can be reformulated as a Least Squares (LS) problem and we exploit a novel meta- algorithm to efficiently solve it. At each iteration the meta-algorithm processes only one dataset. Specifically, it firstly estimates the stochastic LS objective function, by splitting this dataset into two subsets used to train and test the inner algorithm, respectively. Secondly, it performs a stochastic gradient step with the estimated value. Under specific assumptions, we present a bound for the generalization error of our meta-algorithm, which suggests the right splitting parameter to choose. When the hyper-parameters of the problem are fixed, this bound is consistent as the number of tasks grows, even if the sample size is kept constant. Preliminary experiments confirm our theoretical findings, highlighting the advantage of our approach, with respect to independent task learning.
Author Information
Giulia Denevi (IIT/UNIGE)
Carlo Ciliberto (Imperial College London)
Dimitris Stamos (University College London)
Massimiliano Pontil (IIT & UCL)
More from the Same Authors
-
2022 Poster: Conditional Meta-Learning of Linear Representations »
Giulia Denevi · Massimiliano Pontil · Carlo Ciliberto -
2022 Spotlight: Conditional Meta-Learning of Linear Representations »
Giulia Denevi · Massimiliano Pontil · Carlo Ciliberto -
2022 Spotlight: Lightning Talks 3B-1 »
Tianying Ji · Tongda Xu · Giulia Denevi · Aibek Alanov · Martin Wistuba · Wei Zhang · Yuesong Shen · Massimiliano Pontil · Vadim Titov · Yan Wang · Yu Luo · Daniel Cremers · Yanjun Han · Arlind Kadra · Dailan He · Josif Grabocka · Zhengyuan Zhou · Fuchun Sun · Carlo Ciliberto · Dmitry Vetrov · Mingxuan Jing · Chenjian Gao · Aaron Flores · Tsachy Weissman · Han Gao · Fengxiang He · Kunzan Liu · Wenbing Huang · Hongwei Qin -
2022 Poster: Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces »
Vladimir Kostic · Pietro Novelli · Andreas Maurer · Carlo Ciliberto · Lorenzo Rosasco · Massimiliano Pontil -
2021 : Carlo Ciliberto Q&A »
Carlo Ciliberto -
2021 : Carlo Ciliberto »
Carlo Ciliberto -
2021 Poster: PSD Representations for Effective Probability Models »
Alessandro Rudi · Carlo Ciliberto -
2021 Poster: The Role of Global Labels in Few-Shot Classification and How to Infer Them »
Ruohan Wang · Massimiliano Pontil · Carlo Ciliberto -
2020 Poster: Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandits »
Arya Akhavan · Massimiliano Pontil · Alexandre Tsybakov -
2020 Poster: The Advantage of Conditional Meta-Learning for Biased Regularization and Fine Tuning »
Giulia Denevi · Massimiliano Pontil · Carlo Ciliberto -
2020 Poster: Estimating weighted areas under the ROC curve »
Andreas Maurer · Massimiliano Pontil -
2020 Poster: Structured Prediction for Conditional Meta-Learning »
Ruohan Wang · Yiannis Demiris · Carlo Ciliberto -
2020 Poster: Exploiting MMD and Sinkhorn Divergences for Fair and Transferable Representation Learning »
Luca Oneto · Michele Donini · Giulia Luise · Carlo Ciliberto · Andreas Maurer · Massimiliano Pontil -
2019 Poster: Online-Within-Online Meta-Learning »
Giulia Denevi · Dimitris Stamos · Carlo Ciliberto · Massimiliano Pontil -
2019 Poster: Localized Structured Prediction »
Carlo Ciliberto · Francis Bach · Alessandro Rudi -
2019 Poster: Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm »
Giulia Luise · Saverio Salzo · Massimiliano Pontil · Carlo Ciliberto -
2019 Spotlight: Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm »
Giulia Luise · Saverio Salzo · Massimiliano Pontil · Carlo Ciliberto -
2018 Poster: Bilevel learning of the Group Lasso structure »
Jordan Frecon · Saverio Salzo · Massimiliano Pontil -
2018 Spotlight: Bilevel learning of the Group Lasso structure »
Jordan Frecon · Saverio Salzo · Massimiliano Pontil -
2018 Poster: Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance »
Giulia Luise · Alessandro Rudi · Massimiliano Pontil · Carlo Ciliberto -
2018 Poster: Manifold Structured Prediction »
Alessandro Rudi · Carlo Ciliberto · Gian Maria Marconi · Lorenzo Rosasco -
2017 : An Efficient Method to Impose Fairness in Linear Models »
Massimiliano Pontil · John Shawe-Taylor -
2017 Workshop: Workshop on Prioritising Online Content »
John Shawe-Taylor · Massimiliano Pontil · Nicolò Cesa-Bianchi · Emine Yilmaz · Chris Watkins · Sebastian Riedel · Marko Grobelnik -
2017 Poster: Consistent Multitask Learning with Nonlinear Output Relations »
Carlo Ciliberto · Alessandro Rudi · Lorenzo Rosasco · Massimiliano Pontil -
2016 Poster: A Consistent Regularization Approach for Structured Prediction »
Carlo Ciliberto · Lorenzo Rosasco · Alessandro Rudi -
2016 Poster: Mistake Bounds for Binary Matrix Completion »
Mark Herbster · Stephen Pasteris · Massimiliano Pontil -
2015 : The Benefit of Multitask Representation Learning »
Massimiliano Pontil -
2014 Poster: Spectral k-Support Norm Regularization »
Andrew McDonald · Massimiliano Pontil · Dimitris Stamos -
2013 Workshop: New Directions in Transfer and Multi-Task: Learning Across Domains and Tasks »
Urun Dogan · Marius Kloft · Tatiana Tommasi · Francesco Orabona · Massimiliano Pontil · Sinno Jialin Pan · Shai Ben-David · Arthur Gretton · Fei Sha · Marco Signoretto · Rajhans Samdani · Yun-Qian Miao · Mohammad Gheshlaghi azar · Ruth Urner · Christoph Lampert · Jonathan How -
2013 Workshop: Output Representation Learning »
Yuhong Guo · Dale Schuurmans · Richard Zemel · Samy Bengio · Yoshua Bengio · Li Deng · Dan Roth · Kilian Q Weinberger · Jason Weston · Kihyuk Sohn · Florent Perronnin · Gabriel Synnaeve · Pablo R Strasser · julien audiffren · Carlo Ciliberto · Dan Goldwasser -
2013 Poster: A New Convex Relaxation for Tensor Completion »
Bernardino Romera-Paredes · Massimiliano Pontil -
2012 Poster: Optimal kernel choice for large-scale two-sample tests »
Arthur Gretton · Bharath Sriperumbudur · Dino Sejdinovic · Heiko Strathmann · Sivaraman Balakrishnan · Massimiliano Pontil · Kenji Fukumizu -
2010 Spotlight: A Family of Penalty Functions for Structured Sparsity »
Charles A Micchelli · Jean M Morales · Massimiliano Pontil -
2010 Poster: A Family of Penalty Functions for Structured Sparsity »
Charles A Micchelli · Jean M Morales · Massimiliano Pontil -
2008 Poster: Fast Prediction on a Tree »
Mark Herbster · Massimiliano Pontil · Sergio Rojas Galeano -
2008 Oral: Fast Prediction on a Tree »
Mark Herbster · Massimiliano Pontil · Sergio Rojas Galeano -
2008 Poster: On-Line Prediction on Large Diameter Graphs »
Mark Herbster · Massimiliano Pontil · Guy Lever -
2007 Spotlight: A Spectral Regularization Framework for Multi-Task Structure Learning »
Andreas Argyriou · Charles A. Micchelli · Massimiliano Pontil · Yiming Ying -
2007 Poster: A Spectral Regularization Framework for Multi-Task Structure Learning »
Andreas Argyriou · Charles A. Micchelli · Massimiliano Pontil · Yiming Ying -
2006 Poster: Prediction on a Graph with a Perceptron »
Mark Herbster · Massimiliano Pontil -
2006 Spotlight: Prediction on a Graph with a Perceptron »
Mark Herbster · Massimiliano Pontil -
2006 Poster: Multi-Task Feature Learning »
Andreas Argyriou · Theos Evgeniou · Massimiliano Pontil