A Combinatorial Characterization of Online Learning Games with Bounded Losses

07/07/2023

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by   Vinod Raman, et al.

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We study the online learnability of hypothesis classes with respect to arbitrary, but bounded, loss functions. We give a new scale-sensitive combinatorial dimension, named the sequential Minimax dimension, and show that it gives a tight quantitative characterization of online learnability. As applications, we give the first quantitative characterization of online learnability for two natural learning settings: vector-valued regression and multilabel classification.