Bandit Convex Optimization: sqrt{T} Regret in One Dimension

author: Tomer Koren, Technion - Israel Institute of Technology
published: Aug. 20, 2015,   recorded: July 2015,   views: 38
Categories

Slides

Related Open Educational Resources

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.
  Bibliography

Description

We analyze the minimax regret of the adversarial bandit convex optimization problem. Focusing on the one-dimensional case, we prove that the minimax regret is $\widetilde\Theta(\sqrt{T})$ and partially resolve a decade-old open problem. Our analysis is non-constructive, as we do not present a concrete algorithm that attains this regret rate. Instead, we use minimax duality to reduce the problem to a Bayesian setting, where the convex loss functions are drawn from a worst-case distribution, and then we solve the Bayesian version of the problem with a variant of Thompson Sampling. Our analysis features a novel use of convexity, formalized as a ``local-to-global'' property of convex functions, that may be of independent interest.

See Also:

Download slides icon Download slides: colt2015_koren_one_dimension_01.pdf (149.4┬áKB)


Help icon Streaming Video Help

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Write your own review or comment:

make sure you have javascript enabled or clear this field: