The Blessing and the Curse of the Multiplicative Updates
The Blessing and the Curse of the Multiplicative Updates
This chapter shows how replicator dynamics (in a setting with no frequency dependence) correspond to multiplicative updates studied by computer scientists in the context of online learning. The updates learn very quickly (a “blessing”) but they also wipe out potentially valuable variety that may be important when the environment changes (the “curse”). The chapter presents several different techniques developed in machine learning to lift the curse, and also different techniques seen in Nature. The chapter asks what machine learning can learn from Nature and vice versa when the recent past may be a treacherous guide to future events, as exemplified in the disk spin-down problem. Highlights include a demonstration of logical connections between Bayesian updating and replicator dynamics, and a discussion of how in-vitro selection techniques relate to computer algorithms that preserve diversity.
Keywords: replicator dynamics, machine learning, multiplicative updates, relative entropy, in-vitro selection, Bayes“s rule, winnow algorithm, disk spindown problem
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