BISTRO: An Efficient Relaxation-Based Method for Contextual Bandits

Alexander Rakhlin, Karthik Sridharan
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:1977-1985, 2016.

Abstract

We present efficient algorithms for the problem of contextual bandits with i.i.d. covariates, an arbitrary sequence of rewards, and an arbitrary class of policies. Our algorithm BISTRO requires d calls to the empirical risk minimization (ERM) oracle per round, where d is the number of actions. The method uses unlabeled data to make the problem computationally simple. When the ERM problem itself is computationally hard, we extend the approach by employing multiplicative approximation algorithms for the ERM. The integrality gap of the relaxation only enters in the regret bound rather than the benchmark. Finally, we show that the adversarial version of the contextual bandit problem is learnable (and efficient) whenever the full-information supervised online learning problem has a non-trivial regret bound (and efficient).

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-rakhlin16, title = {BISTRO: An Efficient Relaxation-Based Method for Contextual Bandits}, author = {Rakhlin, Alexander and Sridharan, Karthik}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {1977--1985}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/rakhlin16.pdf}, url = {https://proceedings.mlr.press/v48/rakhlin16.html}, abstract = {We present efficient algorithms for the problem of contextual bandits with i.i.d. covariates, an arbitrary sequence of rewards, and an arbitrary class of policies. Our algorithm BISTRO requires d calls to the empirical risk minimization (ERM) oracle per round, where d is the number of actions. The method uses unlabeled data to make the problem computationally simple. When the ERM problem itself is computationally hard, we extend the approach by employing multiplicative approximation algorithms for the ERM. The integrality gap of the relaxation only enters in the regret bound rather than the benchmark. Finally, we show that the adversarial version of the contextual bandit problem is learnable (and efficient) whenever the full-information supervised online learning problem has a non-trivial regret bound (and efficient).} }
Endnote
%0 Conference Paper %T BISTRO: An Efficient Relaxation-Based Method for Contextual Bandits %A Alexander Rakhlin %A Karthik Sridharan %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-rakhlin16 %I PMLR %P 1977--1985 %U https://proceedings.mlr.press/v48/rakhlin16.html %V 48 %X We present efficient algorithms for the problem of contextual bandits with i.i.d. covariates, an arbitrary sequence of rewards, and an arbitrary class of policies. Our algorithm BISTRO requires d calls to the empirical risk minimization (ERM) oracle per round, where d is the number of actions. The method uses unlabeled data to make the problem computationally simple. When the ERM problem itself is computationally hard, we extend the approach by employing multiplicative approximation algorithms for the ERM. The integrality gap of the relaxation only enters in the regret bound rather than the benchmark. Finally, we show that the adversarial version of the contextual bandit problem is learnable (and efficient) whenever the full-information supervised online learning problem has a non-trivial regret bound (and efficient).
RIS
TY - CPAPER TI - BISTRO: An Efficient Relaxation-Based Method for Contextual Bandits AU - Alexander Rakhlin AU - Karthik Sridharan BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-rakhlin16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 1977 EP - 1985 L1 - http://proceedings.mlr.press/v48/rakhlin16.pdf UR - https://proceedings.mlr.press/v48/rakhlin16.html AB - We present efficient algorithms for the problem of contextual bandits with i.i.d. covariates, an arbitrary sequence of rewards, and an arbitrary class of policies. Our algorithm BISTRO requires d calls to the empirical risk minimization (ERM) oracle per round, where d is the number of actions. The method uses unlabeled data to make the problem computationally simple. When the ERM problem itself is computationally hard, we extend the approach by employing multiplicative approximation algorithms for the ERM. The integrality gap of the relaxation only enters in the regret bound rather than the benchmark. Finally, we show that the adversarial version of the contextual bandit problem is learnable (and efficient) whenever the full-information supervised online learning problem has a non-trivial regret bound (and efficient). ER -
APA
Rakhlin, A. & Sridharan, K.. (2016). BISTRO: An Efficient Relaxation-Based Method for Contextual Bandits. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:1977-1985 Available from https://proceedings.mlr.press/v48/rakhlin16.html.

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