Safe Convex Learning under Uncertain Constraints

Ilnura Usmanova, Andreas Krause, Maryam Kamgarpour
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:2106-2114, 2019.

Abstract

We address the problem of minimizing a convex smooth function f(x) over a compact polyhedral set D given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as personalized medicine and robotics. In such cases, one needs to ensure constraints are satisfied while exploring the decision space to find optimum of the loss function. We propose a new variant of the Frank-Wolfe algorithm, which applies to the case of uncertain linear constraints. Using robust optimization, we provide the convergence rate of the algorithm while guaranteeing feasibility of all iterates, with high probability.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-usmanova19a, title = {Safe Convex Learning under Uncertain Constraints}, author = {Usmanova, Ilnura and Krause, Andreas and Kamgarpour, Maryam}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {2106--2114}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/usmanova19a/usmanova19a.pdf}, url = {https://proceedings.mlr.press/v89/usmanova19a.html}, abstract = {We address the problem of minimizing a convex smooth function f(x) over a compact polyhedral set D given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as personalized medicine and robotics. In such cases, one needs to ensure constraints are satisfied while exploring the decision space to find optimum of the loss function. We propose a new variant of the Frank-Wolfe algorithm, which applies to the case of uncertain linear constraints. Using robust optimization, we provide the convergence rate of the algorithm while guaranteeing feasibility of all iterates, with high probability.} }
Endnote
%0 Conference Paper %T Safe Convex Learning under Uncertain Constraints %A Ilnura Usmanova %A Andreas Krause %A Maryam Kamgarpour %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-usmanova19a %I PMLR %P 2106--2114 %U https://proceedings.mlr.press/v89/usmanova19a.html %V 89 %X We address the problem of minimizing a convex smooth function f(x) over a compact polyhedral set D given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as personalized medicine and robotics. In such cases, one needs to ensure constraints are satisfied while exploring the decision space to find optimum of the loss function. We propose a new variant of the Frank-Wolfe algorithm, which applies to the case of uncertain linear constraints. Using robust optimization, we provide the convergence rate of the algorithm while guaranteeing feasibility of all iterates, with high probability.
APA
Usmanova, I., Krause, A. & Kamgarpour, M.. (2019). Safe Convex Learning under Uncertain Constraints. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:2106-2114 Available from https://proceedings.mlr.press/v89/usmanova19a.html.

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