Active Learning for Accurate Estimation of Linear Models

Carlos Riquelme, Mohammad Ghavamzadeh, Alessandro Lazaric
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:2931-2939, 2017.

Abstract

We explore the sequential decision making problem where the goal is to estimate uniformly well a number of linear models, given a shared budget of random contexts independently sampled from a known distribution. The decision maker must query one of the linear models for each incoming context, and receives an observation corrupted by noise levels that are unknown, and depend on the model instance. We present Trace-UCB, an adaptive allocation algorithm that learns the noise levels while balancing contexts accordingly across the different linear functions, and derive guarantees for simple regret in both expectation and high-probability. Finally, we extend the algorithm and its guarantees to high dimensional settings, where the number of linear models times the dimension of the contextual space is higher than the total budget of samples. Simulations with real data suggest that Trace-UCB is remarkably robust, outperforming a number of baselines even when its assumptions are violated.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-riquelme17a, title = {Active Learning for Accurate Estimation of Linear Models}, author = {Carlos Riquelme and Mohammad Ghavamzadeh and Alessandro Lazaric}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {2931--2939}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/riquelme17a/riquelme17a.pdf}, url = {https://proceedings.mlr.press/v70/riquelme17a.html}, abstract = {We explore the sequential decision making problem where the goal is to estimate uniformly well a number of linear models, given a shared budget of random contexts independently sampled from a known distribution. The decision maker must query one of the linear models for each incoming context, and receives an observation corrupted by noise levels that are unknown, and depend on the model instance. We present Trace-UCB, an adaptive allocation algorithm that learns the noise levels while balancing contexts accordingly across the different linear functions, and derive guarantees for simple regret in both expectation and high-probability. Finally, we extend the algorithm and its guarantees to high dimensional settings, where the number of linear models times the dimension of the contextual space is higher than the total budget of samples. Simulations with real data suggest that Trace-UCB is remarkably robust, outperforming a number of baselines even when its assumptions are violated.} }
Endnote
%0 Conference Paper %T Active Learning for Accurate Estimation of Linear Models %A Carlos Riquelme %A Mohammad Ghavamzadeh %A Alessandro Lazaric %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-riquelme17a %I PMLR %P 2931--2939 %U https://proceedings.mlr.press/v70/riquelme17a.html %V 70 %X We explore the sequential decision making problem where the goal is to estimate uniformly well a number of linear models, given a shared budget of random contexts independently sampled from a known distribution. The decision maker must query one of the linear models for each incoming context, and receives an observation corrupted by noise levels that are unknown, and depend on the model instance. We present Trace-UCB, an adaptive allocation algorithm that learns the noise levels while balancing contexts accordingly across the different linear functions, and derive guarantees for simple regret in both expectation and high-probability. Finally, we extend the algorithm and its guarantees to high dimensional settings, where the number of linear models times the dimension of the contextual space is higher than the total budget of samples. Simulations with real data suggest that Trace-UCB is remarkably robust, outperforming a number of baselines even when its assumptions are violated.
APA
Riquelme, C., Ghavamzadeh, M. & Lazaric, A.. (2017). Active Learning for Accurate Estimation of Linear Models. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:2931-2939 Available from https://proceedings.mlr.press/v70/riquelme17a.html.

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