Algorithmic Chaining and the Role of Partial Feedback in Online Nonparametric Learning

Nicolò Cesa-Bianchi, Pierre Gaillard, Claudio Gentile, Sébastien Gerchinovitz
Proceedings of the 2017 Conference on Learning Theory, PMLR 65:465-481, 2017.

Abstract

We investigate contextual online learning with nonparametric (Lipschitz) comparison classes under different assumptions on losses and feedback information. For full information feedback and Lipschitz losses, we design the first explicit algorithm achieving the minimax regret rate (up to log factors). In a partial feedback model motivated by second-price auctions, we obtain algorithms for Lipschitz and semi-Lipschitz losses with regret bounds improving on the known bounds for standard bandit feedback. Our analysis combines novel results for contextual second-price auctions with a novel algorithmic approach based on chaining. When the context space is Euclidean, our chaining approach is efficient and delivers an even better regret bound.

Cite this Paper

BibTeX
@InProceedings{pmlr-v65-cesa-bianchi17a, title = {Algorithmic Chaining and the Role of Partial Feedback in Online Nonparametric Learning}, author = {Cesa-Bianchi, Nicolò and Gaillard, Pierre and Gentile, Claudio and Gerchinovitz, Sébastien}, booktitle = {Proceedings of the 2017 Conference on Learning Theory}, pages = {465--481}, 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/cesa-bianchi17a/cesa-bianchi17a.pdf}, url = {https://proceedings.mlr.press/v65/cesa-bianchi17a.html}, abstract = {We investigate contextual online learning with nonparametric (Lipschitz) comparison classes under different assumptions on losses and feedback information. For full information feedback and Lipschitz losses, we design the first explicit algorithm achieving the minimax regret rate (up to log factors). In a partial feedback model motivated by second-price auctions, we obtain algorithms for Lipschitz and semi-Lipschitz losses with regret bounds improving on the known bounds for standard bandit feedback. Our analysis combines novel results for contextual second-price auctions with a novel algorithmic approach based on chaining. When the context space is Euclidean, our chaining approach is efficient and delivers an even better regret bound.} }
Endnote
%0 Conference Paper %T Algorithmic Chaining and the Role of Partial Feedback in Online Nonparametric Learning %A Nicolò Cesa-Bianchi %A Pierre Gaillard %A Claudio Gentile %A Sébastien Gerchinovitz %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-cesa-bianchi17a %I PMLR %P 465--481 %U https://proceedings.mlr.press/v65/cesa-bianchi17a.html %V 65 %X We investigate contextual online learning with nonparametric (Lipschitz) comparison classes under different assumptions on losses and feedback information. For full information feedback and Lipschitz losses, we design the first explicit algorithm achieving the minimax regret rate (up to log factors). In a partial feedback model motivated by second-price auctions, we obtain algorithms for Lipschitz and semi-Lipschitz losses with regret bounds improving on the known bounds for standard bandit feedback. Our analysis combines novel results for contextual second-price auctions with a novel algorithmic approach based on chaining. When the context space is Euclidean, our chaining approach is efficient and delivers an even better regret bound.
APA
Cesa-Bianchi, N., Gaillard, P., Gentile, C. & Gerchinovitz, S.. (2017). Algorithmic Chaining and the Role of Partial Feedback in Online Nonparametric Learning. Proceedings of the 2017 Conference on Learning Theory, in Proceedings of Machine Learning Research 65:465-481 Available from https://proceedings.mlr.press/v65/cesa-bianchi17a.html.

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