Publication

No Regret Bound for Extreme Bandits

ArXiv PrePrint


Abstract

Algorithms for hyperparameter optimization abound, all of which work well under different and often unverifiable assumptions. Motivated by the general challenge of sequentially choosing which algorithm to use, we study the more specific task of choosing among distributions to use for random hyperparameter optimization. This work is naturally framed in the extreme bandit setting, which deals with sequentially choosing which distribution from a collection to sample in order to minimize (maximize) the single best cost (reward). Whereas the distributions in the standard bandit setting are primarly characterized by their means, a number of subtleties arise when we care about the minimal cost as opposed to the average cost. For example, there may not be a well-defined “best” distribution as there is in the standard bandit setting. The best distribution depends on the rewards that have been obtained and on the remaining time horizon. Whereas in the standard bandit setting, it is sensible to compare policies with an oracle which plays the single best arm, in the extreme bandit setting, there are multiple sensible oracle models. We define a sensible notion of regret in the extreme bandit setting, which turns out to be more subtle than in the standard bandit setting. We then prove that no policy can asymptotically achieve no regret. Furthermore, we show that in the worst case, no policy can be guaranteed to perform better than the policy of choosing each distribution equally often.

Related Publications

All Publications

ARCH: Animatable Reconstruction of Clothed Humans

Zeng Huang, Yuanlu Xu, Christoph Lassner, Hao Li, Tony Tung

CVPR - June 15, 2020

In Defense of Grid Features for Visual Question Answering

Huaizu Jiang, Ishan Misra, Marcus Rohrbach, Erik Learned-Miller, Xinlei Chen

CVPR - June 14, 2020

Hierarchical Scene Coordinate Classification and Regression for Visual Localization

Xiaotian Li, Shuzhe Wang, Yi Zhao, Jakob Verbeek, Juho Kannala

CVPR - June 13, 2020

SynSin: End-to-end View Synthesis from a Single Image

Olivia Wiles, Georgia Gkioxari, Richard Szeliski, Justin Johnson

CVPR - June 14, 2020

To help personalize content, tailor and measure ads, and provide a safer experience, we use cookies. By clicking or navigating the site, you agree to allow our collection of information on and off Facebook through cookies. Learn more, including about available controls: Cookies Policy