TCS-TR-A-05-4

Date: Thu Jul 14 20:03:07 2005

Title: Defensive Universal Learning with Experts

Authors: Jan Poland and Marcus Hutter

Contact:

First name: Jan
Last name: Poland
Address: Graduate School of Information Science and Technology Hokkaido University N-14, W-9 Sapporo 060-0814, Japan
Email: jan@ist.hokudai.ac.jp

Abstract. This paper shows how universal learning can be achieved with expert advice. To this aim, we specify an experts algorithm with the following characteristics: (a) it uses only feedback from the actions actually chosen (bandit setup), (b) it can be applied with countably infinite expert classes, and (c) it copes with losses that may grow in time appropriately slowly. We prove loss bounds against an adaptive adversary. From this, we obtain a master algorithm for "reactive" experts problems, which means that the master's actions may influence the behavior of the adversary. Our algorithm can significantly outperform standard experts algorithms on such problems. Finally, we combine it with a universal expert class. The resulting universal learner performs -- in a certain sense -- almost as well as any computable strategy, for any online decision problem. We also specify the (worst-case) convergence speed, which is very slow.