Unconstrained Online Linear Learning in Hilbert Spaces: Minimax Algorithms and Normal Approximations
published: July 15, 2014, recorded: June 2014, views: 2397
Report a problem or upload filesIf 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.
We study algorithms for online linear optimization in Hilbert spaces, focusing on the case where the player is unconstrained. We develop a novel characterization of a large class of minimax algorithms, recovering, and even improving, several previous results as immediate corollaries. Moreover, using our tools, we develop an algorithm that provides a regret bound of O(UTlog(UT−−√log2T+1)√), where U is the L2 norm of an arbitrary comparator and both T and U are unknown to the player. This bound is optimal up to loglogT√ terms. When T is known, we derive an algorithm with an optimal regret bound (up to constant factors). For both the known and unknown T case, a Normal approximation to the conditional value of the game proves to be the key analysis tool.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !