Prediction with Expert Advice Research

Description

Making rational decisions is a central concern of both science and everyday life. (Polynomials of which degree should I use to fit my data sets? Should I take my umbrella today, tomorrow, etc.? Which stocks should I buy and sell this year?) Only rarely we can readily choose the best course of action; more often we will have a more or less extensive (maybe infinite) family of potentially successful decision strategies. (Whether a decision strategy is successful will depend not only on the merits of this strategy but also on the future events which we do not know yet.) However, at the end of the day we must choose one specific decision strategy, so we naturally arrive at this problem: given a family of decision strategies, find a new decision strategy which will perform, under any circumstances, almost as well as the best (under these circumstances) decision strategy in the family.

At first, this task might appear hopeless for even moderately interesting families of decision strategies. (Recall that we want the constructed decision strategy to perform almost as well as the best strategy in the family always; we do not make any stochastic assumptions about the generation of the future events.) However, for one specific loss function a good merging algorithm has been known for ages (the Bayesian merging scheme) and for many more loss functions good merging algorithms have been found in recent years. CLRC members have been studying the following algorithms and approaches in prediction with expert advice: the aggregating algorithm (including the Bayesian algorithm, the weighted majority algorithm, and the universal portfolio algorithm as special cases), the weak aggregating algorithm, and defensive forecasting.

People

Volodya Vovk
Yuri Kalnichkan
Chris Watkins