No Regret Bound for Extreme Bandits

ArXiv PrePrint


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

Robust Market Equilibria with Uncertain Preferences

Riley Murray, Christian Kroer, Alex Peysakhovich, Parikshit Shah

AAAI - February 12, 2020

Weak-Attention Suppression For Transformer Based Speech Recognition

Yangyang Shi, Yongqiang Wang, Chunyang Wu, Christian Fuegen, Frank Zhang, Duc Le, Ching-Feng Yeh, Michael L. Seltzer

Interspeech - October 26, 2020

Machine Learning in Compilers: Past, Present, and Future

Hugh Leather, Chris Cummins

FDL - September 14, 2020

Unsupervised Cross-Domain Singing Voice Conversion

Adam Polyak, Lior Wolf, Yossi Adi, Yaniv Taigman

Interspeech - August 8, 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