Open Problem: First-Order Regret Bounds for Contextual Bandits

Alekh Agarwal, Akshay Krishnamurthy, John Langford, Haipeng Luo, Schapire Robert E.
Proceedings of the 2017 Conference on Learning Theory, PMLR 65:4-7, 2017.

Abstract

We describe two open problems related to first order regret bounds for contextual bandits. The first asks for an algorithm with a regret bound of $\tilde{\mathcal{O}}(\sqrt{L_⋆}K \ln N)$ where there are $K$ actions, $N$ policies, and $L_⋆$ is the cumulative loss of the best policy. The second asks for an optimization-oracle-efficient algorithm with regret $\tilde{\mathcal{O}}(L_⋆^{2/3}poly(K, \ln(N/δ)))$. We describe some positive results, such as an inefficient algorithm for the second problem, and some partial negative results.

Cite this Paper

BibTeX
@InProceedings{pmlr-v65-agarwal17a, title = {Open Problem: First-Order Regret Bounds for Contextual Bandits}, author = {Agarwal, Alekh and Krishnamurthy, Akshay and Langford, John and Luo, Haipeng and E., Schapire Robert}, booktitle = {Proceedings of the 2017 Conference on Learning Theory}, pages = {4--7}, year = {2017}, editor = {Kale, Satyen and Shamir, Ohad}, volume = {65}, series = {Proceedings of Machine Learning Research}, month = {07--10 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v65/agarwal17a/agarwal17a.pdf}, url = {https://proceedings.mlr.press/v65/agarwal17a.html}, abstract = {We describe two open problems related to first order regret bounds for contextual bandits. The first asks for an algorithm with a regret bound of $\tilde{\mathcal{O}}(\sqrt{L_⋆}K \ln N)$ where there are $K$ actions, $N$ policies, and $L_⋆$ is the cumulative loss of the best policy. The second asks for an optimization-oracle-efficient algorithm with regret $\tilde{\mathcal{O}}(L_⋆^{2/3}poly(K, \ln(N/δ)))$. We describe some positive results, such as an inefficient algorithm for the second problem, and some partial negative results. } }
Endnote
%0 Conference Paper %T Open Problem: First-Order Regret Bounds for Contextual Bandits %A Alekh Agarwal %A Akshay Krishnamurthy %A John Langford %A Haipeng Luo %A Schapire Robert E. %B Proceedings of the 2017 Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2017 %E Satyen Kale %E Ohad Shamir %F pmlr-v65-agarwal17a %I PMLR %P 4--7 %U https://proceedings.mlr.press/v65/agarwal17a.html %V 65 %X We describe two open problems related to first order regret bounds for contextual bandits. The first asks for an algorithm with a regret bound of $\tilde{\mathcal{O}}(\sqrt{L_⋆}K \ln N)$ where there are $K$ actions, $N$ policies, and $L_⋆$ is the cumulative loss of the best policy. The second asks for an optimization-oracle-efficient algorithm with regret $\tilde{\mathcal{O}}(L_⋆^{2/3}poly(K, \ln(N/δ)))$. We describe some positive results, such as an inefficient algorithm for the second problem, and some partial negative results.
APA
Agarwal, A., Krishnamurthy, A., Langford, J., Luo, H. & E., S.R.. (2017). Open Problem: First-Order Regret Bounds for Contextual Bandits. Proceedings of the 2017 Conference on Learning Theory, in Proceedings of Machine Learning Research 65:4-7 Available from https://proceedings.mlr.press/v65/agarwal17a.html.

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