On the Complexity of Bandit Linear Optimization

Ohad Shamir
Proceedings of The 28th Conference on Learning Theory, PMLR 40:1523-1551, 2015.

Abstract

We study the attainable regret for online linear optimization problems with bandit feedback, where unlike the full-information setting, the player can only observe its own loss rather than the full loss vector. We show that the price of bandit information in this setting can be as large as d, disproving the well-known conjecture (Danie et al. (2007)) that the regret for bandit linear optimization is at most \sqrtd times the full-information regret. Surprisingly, this is shown using “trivial” modifications of standard domains, which have no effect in the full-information setting. This and other results we present highlight some interesting differences between full-information and bandit learning, which were not considered in previous literature.

Cite this Paper

BibTeX
@InProceedings{pmlr-v40-Shamir15, title = {On the Complexity of Bandit Linear Optimization}, author = {Shamir, Ohad}, booktitle = {Proceedings of The 28th Conference on Learning Theory}, pages = {1523--1551}, year = {2015}, editor = {Grünwald, Peter and Hazan, Elad and Kale, Satyen}, volume = {40}, series = {Proceedings of Machine Learning Research}, address = {Paris, France}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v40/Shamir15.pdf}, url = {https://proceedings.mlr.press/v40/Shamir15.html}, abstract = {We study the attainable regret for online linear optimization problems with bandit feedback, where unlike the full-information setting, the player can only observe its own loss rather than the full loss vector. We show that the price of bandit information in this setting can be as large as d, disproving the well-known conjecture (Danie et al. (2007)) that the regret for bandit linear optimization is at most \sqrtd times the full-information regret. Surprisingly, this is shown using “trivial” modifications of standard domains, which have no effect in the full-information setting. This and other results we present highlight some interesting differences between full-information and bandit learning, which were not considered in previous literature.} }
Endnote
%0 Conference Paper %T On the Complexity of Bandit Linear Optimization %A Ohad Shamir %B Proceedings of The 28th Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2015 %E Peter Grünwald %E Elad Hazan %E Satyen Kale %F pmlr-v40-Shamir15 %I PMLR %P 1523--1551 %U https://proceedings.mlr.press/v40/Shamir15.html %V 40 %X We study the attainable regret for online linear optimization problems with bandit feedback, where unlike the full-information setting, the player can only observe its own loss rather than the full loss vector. We show that the price of bandit information in this setting can be as large as d, disproving the well-known conjecture (Danie et al. (2007)) that the regret for bandit linear optimization is at most \sqrtd times the full-information regret. Surprisingly, this is shown using “trivial” modifications of standard domains, which have no effect in the full-information setting. This and other results we present highlight some interesting differences between full-information and bandit learning, which were not considered in previous literature.
RIS
TY - CPAPER TI - On the Complexity of Bandit Linear Optimization AU - Ohad Shamir BT - Proceedings of The 28th Conference on Learning Theory DA - 2015/06/26 ED - Peter Grünwald ED - Elad Hazan ED - Satyen Kale ID - pmlr-v40-Shamir15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 40 SP - 1523 EP - 1551 L1 - http://proceedings.mlr.press/v40/Shamir15.pdf UR - https://proceedings.mlr.press/v40/Shamir15.html AB - We study the attainable regret for online linear optimization problems with bandit feedback, where unlike the full-information setting, the player can only observe its own loss rather than the full loss vector. We show that the price of bandit information in this setting can be as large as d, disproving the well-known conjecture (Danie et al. (2007)) that the regret for bandit linear optimization is at most \sqrtd times the full-information regret. Surprisingly, this is shown using “trivial” modifications of standard domains, which have no effect in the full-information setting. This and other results we present highlight some interesting differences between full-information and bandit learning, which were not considered in previous literature. ER -
APA
Shamir, O.. (2015). On the Complexity of Bandit Linear Optimization. Proceedings of The 28th Conference on Learning Theory, in Proceedings of Machine Learning Research 40:1523-1551 Available from https://proceedings.mlr.press/v40/Shamir15.html.

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